INFLECTION NEXUS - SPAINFLECTION NEXUS - SPA (Shadow Portfolio Adaptive)
Foreword: The Living Algorithm
For decades, technical analysis has been a conversation between a trader and a static chart. We apply our indicators with their fixed-length inputs, and we hope that our rigid tools can somehow capture the essence of a market that is fluid, chaotic, and perpetually evolving. When our tools fail, we are told to "adapt." But what if the tools themselves could learn that lesson? What if our indicators could adapt not just for us, but with us?
This script, INFLECTION NEXUS - SPA, is the realization of that vision. It is an advanced analytical framework built around a revolutionary core: the Shadow Portfolio Adaptive (SPA) Engine . The buy and sell signals you see on the chart are an evolution of the logic from my previous work, "Turning Point." However, this is not a simple combination of two scripts. The SPA engine so fundamentally transforms the nature of the analysis that it creates an entirely new class of indicator. This publication is a showcase of that groundbreaking, self-learning engine.
This system is undeniably complex. When you first load it, the sheer volume of information may feel overwhelming. That is a testament to the depth of its analysis. This guide is designed to be your comprehensive manual, to break down every single component, every color, every number, into simple, understandable concepts. By the end of this document, you will not only master its functions but will also possess a deeper understanding of the market dynamics it is designed to reveal.
Chapter 1: The Paradigm Shift - Why the SPA Engine is a Leap Forward
To grasp the innovation here, we must first deconstruct the severe limitations of traditional "adaptive" indicators.
Part A: The Traditional Model - Driving by the Rear-View Mirror
Conventional "adaptive" systems are fundamentally reactive. They operate on a slow, inefficient loop: they wait for their own specific, biased signal to fire, wait for that trade to close, and only after a long and statistically significant "warm-up" period of 50-100 trades do they finally make a small, retrospective adjustment. They are always adapting to a market that no longer exists.
Part B: The SPA Model - The Proactive Co-Pilot
The Shadow Portfolio Adaptive (SPA) engine is a complete re-imagining of this process. It is not reactive; it is proactive, data-saturated, and instantly aware.
Continuous, Unbiased Learning: The SPA engine does not wait for a signal to learn. Its Shadow Portfolio is constantly running 5-bar long and short trades in the background. It learns from every single 5-bar slice of market action , giving it a continuous, unbiased stream of performance data. It is the difference between reading a textbook chapter and having a live sparring partner in the ring 24/7.
Instantaneous Market Awareness - The End of the "Warm-Up": This is the critical innovation. The SPA engine does not require a 100-trade warm-up period. The learning does not start after 50 trades; it begins on the 6th bar of the chart when the first shadow trade closes. From that moment on, the system is market-aware, analyzing data, and capable of making intelligent adjustments. The SPA engine is not adapting to old wins and losses. It is adapting, in near real-time, to the market's ever-shifting character, volatility, and personality.
Chapter 2: The Anatomy of the SPA Engine - A Granular Deep Dive
The engine is composed of three primary systems that work in a sophisticated, interconnected symphony.
Section 1: The Shadow Portfolio (The Information Harvester)
What it is, Simply: Think of this as the script's eyes and ears. It's a team of 10 virtual traders (5 long, 5 short) who are constantly taking small, quick trades to feel out the market.
How it Works, Simply: On every new bar, a new "long" trader and a new "short" trader enter the market. Exactly 5 bars later, they close their positions. This cycle is perpetual and relentless.
The Critical 'Why': Because these virtual traders enter and exit based on a fixed time (5 bars), not on a "good" or "bad" signal, their results are completely unbiased . They are simply measuring: "What happened to price over the last 5 bars?" This provides the raw, untainted truth about the market's behavior that the rest of the system needs to learn effectively.
The Golden Metric (ATR Normalization): The engine doesn't just look at dollar P&L. It's smarter than that. It asks a more intelligent question: "How much did this trade make relative to the current volatility?"
Analogy: Imagine a flea and an elephant. If they both jump 1 inch, who is more impressive? The flea. The SPA engine understands this. A $10 profit when the market is dead quiet is far more significant than a $10 profit during a wild, volatile swing.
The Formula: realized_atr = (close - trade.entry) / trade.atr_entry. It takes the raw profit and divides it by the Average True Range (a measure of volatility) at the moment of entry. This gives a pure, "apples-to-apples" score for every single trade, which is the foundational data point for all learning.
Section 2: The Cognitive Map (The Long-Term Brain)
What it is, Simply: This is the engine's deep memory, its library of experiences. Imagine a giant, 64-square chessboard (8x8 grid). Each square on the board represents a very specific type of market environment.
The Two Dimensions of Thought (The 'How'): How does it know which square we are on? It looks at two things:
The Market's Personality (X-Axis): Is the market behaving like a disciplined soldier, marching in a clear trend? Or is it like a chaotic, unpredictable child, running all over the place? The engine calculates a "Regime" score to figure this out.
The Market's Energy Level (Y-Axis): Is the market sleepy and quiet, or is it wide-awake and hyperactive? The engine measures "Normalized Volatility" to determine this.
The Power of Generalization (The 'Why'): When a Shadow Portfolio trade closes, its result is recorded in the corresponding square on the chessboard. But here's the clever part: it also shares a little bit of that lesson with the squares immediately next to it (using a Gaussian Kernel).
Analogy: If you touch a hot stove and learn "don't touch," your brain is smart enough to know you probably shouldn't touch the hot oven door next to it either, even if you haven't touched it directly. The Cognitive Map does the same thing, allowing it to make intelligent inferences even in market conditions it has seen less frequently. Each square remembers what indicator settings worked best in that specific environment.
Section 3: The Adaptive Engine (The Central Nervous System)
What it is, Simply: This is the conductor of the orchestra. It takes information from all other parts of the system and decides exactly what to do.
The Symphony of Inputs: It listens to three distinct sources of information before making a decision:
The Short-Term Memory (Rolling Stats): It looks at the performance of the last rollN shadow trades. This is its immediate, recent experience.
The Long-Term Wisdom (Cognitive Map): It consults the grand library of the Cognitive Map to see what has worked best in the current market type over the long haul.
The Gut Instinct (Bin Learning): It keeps a small "mini-batch" of the most recent trades. If this batch shows a very strong, sudden pattern, it can trigger a rapid, reflexive adjustment, like pulling your hand away from a flame.
The Fusion Process: It then blends these three opinions together in a sophisticated way. It gives more weight to the opinions it's more confident in (e.g., a Cognitive Map square with hundreds of trades of experience) and uses your Adaptation Intensity (dialK) input to decide how much to listen to its "gut instinct." The final decision is then smoothed to ensure the indicator's parameters change in a stable, intelligent way.
Chapter 3: The Control Panel - A Novice's Guide to Every Input
This is the most important chapter. Let's break down what these confusing settings actually do in the simplest terms possible.
--- SECTION 1: THE DRIVER'S SEAT (SIGNAL ENGINE & BASE SETTINGS) ---
🧾 Signal Engine (Turning Point):
What it is: These are the rules for the final BUY and SELL signs.
Think of it like this: The SPA engine is the smart robot that tunes your race car. These settings are you, the driver, telling the robot what kind of race you're in.
Enable Reversal Mode: You tell the robot, "I want to race on a curvy track with lots of turns." The robot will tune the car to be agile for catching tops and bottoms.
Enable Breakout Mode: You tell the robot, "I want to race on a long, straight track." The robot will tune the car for pure speed to follow the trend.
Require New Extreme: This is a quality filter. It tells the driver, "Don't look for a turn unless we've just hit a new top speed on the straightaway." It makes sure the reversal is from a real extreme.
Min Bars Between Signals: This is the "pit stop" rule. You're telling the robot, "After you show me a sign, wait at least 10 bars before showing another one, so I don't get confused."
⚡ ATR Bands (Base Inputs):
What they are: These are the starting settings for your car before the robot starts tuning it. These are your factory defaults.
Sensitivity: This is the "Bump Detector." A low number means the car feels every tiny pebble on the road. A high number means it only notices the big speed bumps. You want to set it so it notices the important bumps (real market structure) but ignores the pebbles (noise).
ATR Period & Multiplier: These set the starting size of the "safety lane" (the green and blue bands) around your car. The robot's main job is to constantly adjust the size of this safety lane to perfectly fit the current road conditions.
📊 & 📈 Filter Settings (RSI & Volume):
What they are: These are your co-pilot's confirmation checks.
Enable RSI Filter: Your co-pilot will check the "Engine Temperature" (RSI). He won't let you hit the gas (BUY) if the engine is already overheating (overbought).
RSI Length & Lookbacks: These tune how your co-pilot's temperature gauge works. The defaults are standard.
Require Volume Spike: Your co-pilot will check the "Crowd Noise" (Volume). He won't give you a signal unless he hears the crowd roar, confirming that a lot of people are interested in this move.
🎯 Signal Quality Control:
Enable Major Levels Only: This tells your co-pilot to be extra picky. He will only confirm signals that happen after a huge, powerful move, ignoring all the small stuff.
--- SECTION 2: THE ROBOT'S BRAIN (ENGINE & LEARNING CONTROLS) ---
🎛️ Master Control:
Adaptation Intensity (dialK): THIS IS THE ROBOT'S PERSONALITY DIAL.
Turn it DOWN (1-5): The robot becomes a "Wise Old Professor." It thinks very slowly and carefully, gathers lots of data, and only makes a change when it is 100% sure. Its advice is very reliable but might come a little late.
Turn it UP (15-20): The robot becomes a "Hyper-Reactive Teenager." It has a short attention span, reacts instantly to everything it sees, and changes its mind constantly. It's super-fast to new information but might get faked out a lot.
The Default (10): A "Skilled Professional." The perfect balance of thoughtful and responsive. Start here.
🧠 Adaptive Engine:
Enable Adaptive System: This is the main power button for your robot. Turn it off, and you're driving a normal, non-smart car. Turn it on, and the robot takes over the tuning.
Use Shadow Cycle: This turns on the robot's "practice laps." The robot can't learn without practicing. This must be on for the robot to work.
Lock ATR Bands: This is a visual choice. "Locked" means the safety lanes on your screen stay where your factory defaults put them (the robot still makes changes to the signals in the background). "Unlocked" means you see the safety lanes moving and changing shape in real-time as the robot tunes them.
🎯 Learning (Global + Risk):
What they are: These are the deep-level settings for how your robot's brain processes information.
Rolling Window Size: This is the robot's "Short-Term Memory." How many of the last few practice laps should it remember? A small number means it only cares about what just happened. A big number means it remembers the last hour of practice.
Learn Rate & Smooth Alpha: This is "How big of a change should the robot make?" and "How smoothly should it make the change?" Think of it as turning the steering wheel. A high learn rate is like yanking the wheel; a low one is like a gentle turn. The smoothing makes sure the turn is graceful.
WinRate Thresholds & PnL Cap: These are rules for the robot's learning. They tell it what a "good" or "bad" outcome looks like and tell it to ignore crazy, once-in-a-lifetime events so its memory doesn't get corrupted.
--- SECTION 3: THE GARAGE (RISK, MEMORY & VISUALS) ---
⚠️ Risk Management:
What they are: These are safety rules you can give to your co-pilot for your own awareness. They appear on the dashboard.
The settings: You can set a max number of trades, a max loss for the day, and a "time out" period after a few losses.
Apply Risk to Shadow: This is an important switch. If you turn this ON, your safety rules also apply to the robot's practice laps. If you hit your max loss, the robot stops practicing and learning. It's recommended to leave this OFF so the robot can learn 24/7, even if you have stopped trading.
🗺️ Cognitive Map, STM & Checkpoints:
What it is: The robot's "Long-Term Memory" or its entire library of racing experience.
Use Cognitive Map & STM: These switches turn on the long-term and short-term memory banks. You want these on for the smartest robot.
Map Settings (Grid, Sigma, Half-Life): These are very advanced settings for neuroscientists. They control how the robot's brain is structured and how it forgets old information. The defaults are expertly tuned.
The Checkpoint System: This is the "Save Your Game" button for the robot.
To Save: Check Emit Checkpoint Now. Go to your alert log, and you will see a very long password. Copy this password.
To Load: Paste that password into the Memory Checkpoint box. Then, check Apply Checkpoint On Next Bar. The robot will instantly download all of its saved memories and experience.
🎨 Visuals & 🧩 Display Params:
What they are: These are all about how your screen looks.
You can control everything: The size and shape of the little diamonds (Entry Orbs), whether you see the purple Adapt Pulse, and where the Dashboards appear on your screen. You can change the Theme to Dark, Light, or Neon. These settings don't change how the robot thinks, only how it presents its information to you.
Chapter 4: The Command Center - Decoding the Dashboard
PANEL A (INFLECTION NEXUS): Your high-level mission control, showing the engine's classification of the current Market Context and the performance summary of the Shadow Portfolio.
PANEL B (SHADOW PORTFOLIO ADAPTIVE): Your deep diagnostic screen.
Performance Metrics: View advanced risk-adjusted stats like the Sharpe Ratio to understand the quality of the market movements the engine is learning from.
Adaptive Parameters (Live vs Base): THIS IS THE MOST CRITICAL SECTION. It shows the engine's Live parameters right next to your (Base) inputs. When the Live values deviate, the engine is communicating its learned wisdom to you. For example, a Live ATR Multiplier of 2.5 versus your Base of 1.4 is the engine telling you: "Caution. The market is currently experiencing high fake-outs and requires giving positions more room to breathe." This section is a direct translation of the engine's learning into actionable insight.
Chapter 5: Reading the Canvas - On-Chart Visuals
The Bands (Green/Blue Lines): These are not static Supertrend lines. They are the physical manifestation of the engine's current thinking. As the engine learns and adapts its ATR Period and Multiplier, you will see these bands widen, tighten, and adjust their distance from price. They are alive.
The Labels (BUY/SELL): These are the final output of the "Turning Point" logic, now supercharged and informed by the fully adaptive SPA engine.
The Purple Pulse (Dot and Background Glow): This is your visual cue that the engine is "thinking." Every time you see this pulse, it means the SPA has just completed a learning cycle and updated its parameters. It is actively recalibrating itself to the market.
Chapter 6: A Manifesto on Innovation and Community
I want to conclude with a personal note on why I dedicate countless hours to building systems like this and sharing them openly.
My purpose is to drive innovation, period. I am not in this space to follow the crowd or to re-package old ideas. The world does not need a 100th version of a slightly modified MACD. Real progress, real breakthroughs, come from venturing into the wilderness, from asking "what if?" and from pursuing concepts that lie at the very edge of possibility.
I am not afraid of being wrong. I am not afraid of being bested by my peers. In fact, I welcome it. If another developer takes an idea from this engine, improves it, and builds something even more magnificent, that is a profound win for our entire community. The only failure I recognize is the failure to try. The only trap I fear is the creative complacency of producing sterile, recycled work just to appease the status quo.
I love this community, and I believe with every fiber of my being that we have barely scratched the surface of what can be discovered and created. This script is my contribution to that shared journey. It is a tool, an idea, and a challenge to all of us: let's keep pushing.
DISCLAIMER: This script is an advanced analytical tool provided for educational and research purposes ONLY. It does not constitute financial advice. All trading involves substantial risk of loss. Past performance is not indicative of future results. Please use this tool responsibly and as part of a comprehensive trading plan.
As the great computer scientist Herbert A. Simon, a pioneer of artificial intelligence, famously said:
"Learning is any process by which a system improves performance from experience."
*Tooltips were updated with a comprehensive guide
May this engine enhance your experience.
— Dskyz, for DAFE Trading Systems
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Sector Rotation & Money Flow Dashboard📊 Overview
The Sector Rotation & Money Flow Dashboard is a comprehensive market analysis tool that tracks 39 major sector ETFs in real-time, providing institutional-grade insights into sector rotation, momentum shifts, and money flow patterns. This indicator helps traders identify which sectors are attracting capital, which are losing favor, and where the next opportunities might emerge.
Perfect for swing traders, position traders, and investors who want to stay ahead of sector rotation and ride the strongest trends while avoiding weak sectors.
🎯 What This Indicator Does
Tracks 39 Major Sectors: From technology to utilities, cryptocurrencies to commodities
Calculates Multiple Timeframes: 1-week, 1-month, 3-month, and 6-month performance
Advanced Momentum Metrics: Proprietary momentum score and acceleration calculations
Relative Strength Analysis: Compare sector performance against any benchmark index
Money Flow Signals: Visual indicators showing where institutional money is moving
Smart Filtering: Pre-built strategy filters for different trading styles
Trend Detection: Emoji-based visual system for quick trend identification
💡 Key Features
1. Performance Metrics
Multiple timeframe analysis (1W, 1M, 3M, 6M)
Month-over-month change tracking
Relative strength vs benchmark index
2. Advanced Analytics
Momentum Score: Weighted composite of recent performance
Acceleration: Rate of change in momentum (second derivative)
Money Flow Signals: IN/OUT/TURN/WATCH indicators
3. Strategy Preset Filters
🎯 Swing Trade: High momentum opportunities
📈 Trend Follow: Established uptrends
🔄 Mean Reversion: Oversold bounce candidates
💎 Value Hunt: Deep value opportunities
🚀 Breakout: Emerging strength
⚠️ Risk Off: Sectors to avoid
4. Customization
All 39 sector ETFs can be customized
Adjustable benchmark index
Flexible display options
Multiple sorting methods
📋 Settings Documentation
Display Settings
Show Table (Default: On)
Toggles the entire dashboard display
Table Position (Default: Middle Center)
Choose from 9 positions on your chart
Options: Top/Middle/Bottom × Left/Center/Right
Rows to Show (Default: 15)
Number of sectors displayed (5-40)
Useful for focusing on top/bottom performers
Sort By (Default: Momentum)
1M/3M/6M: Sort by specific timeframe performance
Momentum: Weighted recent performance score
Acceleration: Rate of momentum change
1M Change: Month-over-month improvement
RS: Relative strength vs benchmark
Flow: IN First: Prioritize sectors with inflows
Flow: TURN First: Focus on reversal candidates
Recovery Plays: Oversold sectors recovering
Oversold Bounce: Deepest declines with positive signs
Top Gainers/Losers 3M: Best/worst quarterly performers
Best Acc + Mom: Combined strength score
Worst Acc (Topping): Sectors losing momentum
Filter Settings
Strategy Preset Filter (Default: All)
All: No filtering
🎯 Swing Trade: Mom >5, Acc >2, Money flowing in
📈 Trend Follow: Positive 1M & 3M, RS >0
🔄 Mean Reversion: Oversold but improving
💎 Value Hunt: Down >10% with recovery signs
🚀 Breakout: Rapid momentum surge
⚠️ Risk Off: Declining or topping sectors
Custom Flow Filter: Use manual flow filter
Custom Flow Signal Filter (Default: All)
Only active when Strategy Preset = "Custom Flow Filter"
IN Only: Strong inflows
TURN Only: Reversal signals
WATCH Only: Recovery candidates
OUT Only: Outflow sectors
Active Flows Only: Any non-neutral signal
Hide Low Volume ETFs (Default: Off)
Filters out illiquid sectors (future enhancement)
Visual Settings
Show Trend Emojis (Default: On)
🚀 Breakout (Strong 1M + High Acceleration)
🔥 Hot Recovery (From -10% to positive)
💪 Steady Uptrend (All timeframes positive)
➡️ Sideways/Ranging
⚠️ Warning/Topping (Up >15%, now slowing)
📉 Falling (Negative + declining)
🔄 Bottoming (Improving from lows)
Compact Mode (Default: Off)
Removes decimals for cleaner display
Useful when showing many rows
Min Data Points Required (Default: 3)
Minimum data points needed to display a sector
Prevents showing sectors with insufficient data
Relative Strength Settings
RS Benchmark Index (Default: AMEX:SPY)
Index to compare all sectors against
Can use SPY, QQQ, IWM, or any other index
RS Period (Days) (Default: 21)
Lookback period for RS calculation
21 days = 1 month, 63 days = 3 months, etc.
Sector ETF Settings (Groups 1-39)
Each sector has two inputs:
Symbol: The ticker (e.g., "AMEX:XLF")
Name: Display name (e.g., "Financials")
All 39 sectors can be customized to track different ETFs or markets.
📈 Column Explanations
Sector: ETF name/description
1M%: 1-month (21-day) performance
3M%: 3-month (63-day) performance
6M%: 6-month (126-day) performance
Mom: Momentum score (weighted average, recent-biased)
Acc: Acceleration (momentum rate of change)
Δ1M: Month-over-month change
RS: Relative strength vs benchmark
Flow: Money flow signal
↗️ IN: Strong inflows
🔄 TURN: Potential reversal
👀 WATCH: Recovery candidate
↘️ OUT: Outflows
—: Neutral
🎮 Usage Tips
For Swing Traders (3-14 days)
Use "🎯 Swing Trade" filter
Sort by "Acceleration" or "Momentum"
Look for Flow = "IN" and Mom >10
Confirm with positive RS
For Position Traders (2-8 weeks)
Use "📈 Trend Follow" filter
Sort by "RS" or "Best Acc + Mom"
Focus on consistent green across timeframes
Ensure RS >3 for market leaders
For Value Investors
Use "💎 Value Hunt" filter
Sort by "Recovery Plays" or "Top Losers 3M"
Look for improving Δ1M
Check for "WATCH" or "TURN" signals
For Risk Management
Regularly check "⚠️ Risk Off" filter
Sort by "Worst Acc (Topping)"
Review holdings for ⚠️ warning emojis
Exit sectors showing "OUT" flow
Market Regime Recognition
Bull Market: Many sectors showing "IN" flow, positive RS
Bear Market: Widespread "OUT" flows, negative RS
Rotation: Mixed flows, some "IN" while others "OUT"
Recovery: Multiple "TURN" and "WATCH" signals
🔧 Pro Tips
Combine Filters + Sorting: Filter first to narrow candidates, then sort to prioritize
Multi-Timeframe Confirmation: Best setups show alignment across 1M, 3M, and momentum
RS is Key: Sectors outperforming SPY (RS >0) tend to continue outperforming
Acceleration Matters: Positive acceleration often precedes price breakouts
Flow Transitions: "WATCH" → "TURN" → "IN" progression identifies new trends early
Regular Scans:
Daily: Check "Acceleration" sort
Weekly: Review "1M Change"
Monthly: Analyze "RS" shifts
Divergence Signals:
Price up but Acceleration down = Potential top
Price down but Acceleration up = Potential bottom
Sector Pairs Trading: Long sectors with "IN" flow, short sectors with "OUT" flow
⚠️ Important Notes
This indicator makes 40 security requests (maximum allowed)
Best used on Daily timeframe
Data updates in real-time during market hours
Some ETFs may show "—" if data is unavailable
🎯 Common Strategies
"Follow the Flow"
Only trade sectors showing "IN" flow with positive RS
"Rotation Catcher"
Focus on "TURN" signals in sectors down >15% from highs
"Momentum Rider"
Trade top 3 sectors by Momentum score, exit when Acceleration turns negative
"Mean Reversion"
Buy sectors in bottom 20% by 3M performance when Δ1M improves
"Relative Strength Leader"
Maintain positions only in sectors with RS >5
Not financial advice - always do additional research
Inflection PointInflection Point - The Adaptive Confluence Reversal Engine
This is not just another peak and valley indicator; it is a complete and total reimagining of how market turning points are detected, qualified, and acted upon. Born from the foundational concepts explored in systems like my earlier creation, DAFE - Turning Point, Inflection Point is a ground-up engineering feat designed for the modern trader. It moves beyond static rules and simple pattern recognition into the realm of dynamic, multi-factor confluence analysis and adaptive machine learning.
Where other indicators provide a guess, Inflection Point provides a probability. It meticulously analyzes the market's deepest currents—momentum, exhaustion, and reversal velocity—and fuses them into a single, unified "Confluence Score." This is not a simple combination of indicators; it is an intelligent, weighted system where each component works in concert, creating an analytical engine that is orders of magnitude more sophisticated and reliable than any standard reversal tool.
Furthermore, Inflection Point learns. Through its advanced Adaptive Learning Engine, it constantly monitors its own performance, adjusting its confidence and selectivity in real-time based on its recent success rate. This allows it to adapt its behavior to any security, on any timeframe, with remarkable success.
Theoretical Foundation - Confluence Core
Inflection Point's predictive power does not come from a single, magical formula. It comes from the intelligent synthesis of three critical market phenomena, weighted and scored in real-time to generate a single, high-conviction probability rating.
1. Factor One: Pre-Reversal Momentum State (RSI Analysis)
Instead of reacting to a simple RSI cross, Inflection Point proactively scans for the build-up of momentum that precedes a reversal.
• Formulaic Concept: It measures the highest RSI value over a lookback period for peaks and the lowest RSI for valleys. A signal is only considered valid if significant momentum has been established before the turn, indicating a stretched market condition ripe for reversal.
• Asymmetric Sophistication: The engine uses different, optimized thresholds for bull and bear momentum, recognizing that markets often fall faster than they rise.
2. Factor Two: Volatility Exhaustion (Bollinger Band Analysis)
A true reversal often occurs when price makes a final, exhaustive push into unsustainable territory.
• Formulaic Concept: The engine detects when price has significantly pierced the outer Bollinger Bands. This is not just a touch, but a statistical deviation from the mean that signals volatility exhaustion, where the energy for the current move is likely depleted.
3. Factor Three: Reversal Strength (Rate of Change Analysis)
The character of a reversal matters. A sharp, decisive turn is more significant than a slow, meandering one.
• Formulaic Concept: Using a short-term Rate of Change (ROC), the engine measures the velocity of the reversal itself. A higher ROC score adds significant weight to the final probability, confirming that the new direction has conviction.
4. The Final Calculation: The Adaptive Learning Engine
This is the system's "brain." It maintains a history of its past signals and calculates its real-time win rate. This hitRate is then used to generate an adaptiveMultiplier.
• Self-Correction: In "Quality Control" mode, a high win rate makes the indicator more selective, demanding a higher probability score to issue a signal, thereby protecting streaks. A lower win rate makes it slightly less selective to ensure it continues learning from new market conditions.
• The result is a system that is not static, but a living, breathing tool that adapts its personality to the unique rhythm of any chart.
Why Inflection Point is a Paradigm Shift
Inflection Point is fundamentally different from other reversal indicators for three key reasons:
Confluence Over Isolation: Standard indicators look at one thing (e.g., RSI > 70). Inflection Point simultaneously analyzes momentum, volatility, and velocity, understanding that true reversals are a product of multiple converging factors. It answers not just "if," but "why" a reversal is likely.
Probabilistic Over Binary: Other tools give you a simple "yes" or "no." Inflection Point provides a probability score from 0-100, allowing you to gauge the conviction of every potential signal. This empowers you to differentiate between a weak setup and an A+ opportunity.
Adaptive Over Static: Every other indicator uses the same rules forever. Inflection Point's Adaptive Engine means it is constantly refining its own logic based on what is actually working in the current market, on the specific asset you are trading. It is tailored to the now.
The Inputs Menu - Your Command Center
Every setting is a lever of control, allowing you to tune the engine to your precise trading style and market focus.
🧠 Neural Core Engine
Analysis Depth: This is the primary lookback for the Bollinger Band and other core calculations. A shorter depth makes the indicator faster and more sensitive, ideal for scalping. A longer depth makes it slower and more stable, ideal for swing trading.
Minimum Probability %: This is your master signal filter. It sets the minimum Confluence Score required to plot a signal. Higher values (85-95) will give you only the highest-conviction A+ setups. Lower values (70-80) will show more potential opportunities.
🤖 Adaptive Neural Learning
Enable Adaptive Learning Engine: Toggles the entire learning system. Disabling it will make the indicator's logic static.
Peak/Valley Success Threshold (ATR): This defines what constitutes a "successful" trade for the learning engine. A value of 1.5 means price must move 1.5x the ATR in your favor for the signal to be marked as a win. Adjust this to match your personal take-profit strategy.
Adaptive Mode: This dictates how the engine uses its hitRate. "Quality Control" is recommended for its intelligent filtering. "Aggressive" will always boost signal scores, useful for finding more setups in a known, trending environment.
Asymmetric Balance: Allows you to apply a "boost" to either peak (short) or valley (long) signals. If you find the market you're trading has stronger long reversals, you can increase the "Valley Signal Boost" to catch them more effectively.
🛡️ Elite Filters
Market Noise Filter: An exceptional tool for avoiding choppy markets. It counts the number of directional changes in the last 5 bars. If the market is whipping back and forth too much, it will block the signal. Lower the "Max Direction Changes" to be extremely selective.
Volume Filter: Requires signal confirmation from a significant volume spike. The "Volume Multiplier" dictates how large this spike must be (e.g., 1.2 = 20% above average volume). This is invaluable for filtering out low-conviction moves in stocks and crypto.
The Dashboard - Your Analytical Co-Pilot
The dashboard is not just a set of numbers; it is a holistic overview of the market's health and the engine's current state.
Unified AI Score: This section provides the most critical, at-a-glance information. "Total Score" is the current probability reading, while "Quality" gives you a human-readable interpretation. "Win Rate" shows the real-time performance of the Adaptive Engine.
Order Flow (OFPI): This measures the "weight" of money behind recent price moves by analyzing price change relative to volume. A high positive OFPI suggests strong buying pressure, while a high negative value suggests strong selling pressure. It gives you a peek into the market's underlying flow.
Component Analysis: This allows you to see the individual "Peak" and "Valley" confidence scores before they are filtered, giving you insight into building momentum before a signal forms.
Market Structure: This panel assesses the broader environment. "HTF Trend" tells you the direction of the larger trend (based on EMAs), while "Vol Regime" tells you if the market is in a high, medium, or low volatility state. Use this to align your signals with the broader market context.
Filter & Engine Statistics: Available on the "Large" dashboard, this provides deep insight into how many signals are being blocked by your filters and the current status of the Adaptive Engine's multiplier.
The Visual Interface - A Symphony of Data
Every visual element on the chart is designed for instant interpretation and insight.
Signal Markers: Simple, clean triangles mark the exact bar of a valid signal. A box is drawn around the high/low of the signal bar to highlight the precise point of inflection.
Dynamic Support/Resistance Zones: These are the glowing lines on your chart. They are not static lines; they are dynamic levels that represent the current battlefield between buyers and sellers.
Cyber Cyan (Valley Blue): This is the current Support Zone. This is the price level the market is currently trying to defend.
Neural Pink (Peak Red): This is the current Resistance Zone. This is the price level the market is currently trying to break through.
Grey (Next Level): This line is a projection, based on the current momentum and the size of the S/R range, of where the next major level of conflict will likely be. It acts as a potential price target.
Development & Philosophy
Inflection Point was not assembled; it was engineered. It represents hundreds of hours of research into market dynamics, statistical analysis, and machine learning principles. The goal was to create a tool that moves beyond the limitations of traditional technical analysis, which often fails in modern, algorithm-driven markets. By building a system based on multi-factor confluence and self-adaptive logic, Inflection Point provides a quantifiable, statistical edge that is simply unattainable with simpler tools. This is the result of a relentless pursuit of a better, more intelligent way to trade.
Universal Applicability
The principles of momentum, exhaustion, and velocity are universal to all freely traded markets. Because of its adaptive core and robust filtering options, Inflection Point has proven to be exceptionally effective on any security (stocks, crypto, forex, indices, futures) and on any timeframe (from 1-minute scalping charts to daily swing trading charts).
" Markets are constantly in a state of uncertainty and flux and money is made by discounting the obvious and betting on the unexpected. "
— George Soros
Trade with insight. Trade with anticipation.
— Dskyz, for DAFE Trading Systems
Hosoda’s CloudsMany investors aim to develop trading systems with a high win rate, mistakenly associating it with substantial profits. In reality, high returns are typically achieved through greater exposure to market trends, which inevitably lowers the win rate due to increased risk and more volatile conditions.
The system I present, called “Hosoda’s Clouds” in honor of Goichi Hosoda , the creator of the Ichimoku Kinko Hyo indicator, is likely one of the first profitable systems many traders will encounter. Designed to capture trends, it performs best in markets with clear directional movements and is less suitable for range-bound markets like Forex, which often exhibit lateral price action.
This system is not recommended for low timeframes, such as minute charts, due to the random and emotionally driven nature of price movements in those periods. For a deeper exploration of this topic, I recommend reading my article “Timeframe is Everything”, which discusses the critical importance of selecting the appropriate timeframe.
I suggest testing and applying the “Hosoda’s Clouds” strategy on assets with a strong trending nature and a proven track record of performance. Ideal markets include Tesla (1-hour, 4-hour, and daily), BTC/USDT (daily), SPY (daily), and XAU/USD (daily), as these have consistently shown clear directional trends over time.
Commissions and Configuration
Commissions can be adjusted in the system’s settings to suit individual needs. For evaluating the effectiveness of “Hosoda’s Clouds,” I’ve used a standard commission of $1 per order as a baseline, though this can be modified in the code to accommodate different brokers or preferences.
The margin per trade is set to $1,000 by default, but users are encouraged to experiment with different margin settings in the configuration to match their trading style.
Rules of the “Hosoda’s Clouds” System (Bullish Strategy)
This strategy is designed to capture trending movements in bullish markets using the Ichimoku Kinko Hyo indicator. The rules are as follows:
Long Entry: A long position is triggered when the Tenkan-sen crosses above the Kijun-sen below the Ichimoku cloud, identifying potential reversals or bounces in a bearish context.
Stop Loss (SL): Placed at the low of the candle 12 bars prior to the entry candle. This setting has proven optimal in my tests, but it can be adjusted in the code based on risk tolerance.
Take Profit (TP): The position is closed when the Tenkan-sen crosses below the bottom of the Ichimoku cloud (the minimum of Senkou Span A and Senkou Span B).
Notes on the Code
margin_long=0: Ideal for strategies requiring a fixed position size, particularly useful for manual entries or testing with a constant capital allocation.
margin_long=100: Recommended for high-frequency systems where positions are closed quickly, simulating gradual growth based on realized profits and reflecting real-world broker constraints.
System Performance
The following performance metrics account for $1 per order commissions and were tested on the specified assets and timeframes:
Tesla (H1)
Trades: 148
Win Rate: 29.05%
Period: Jan 2, 2014 – Jan 6, 2020 (+172%)
Simple Annual Growth Rate: +34.3%
Trades: 130
Win Rate: 30.77%
Period: Jan 2, 2020 – Sep 24, 2025 (+858.90%)
Simple Annual Growth Rate: +150.7%
Tesla (H4)
Trades: 102
Win Rate: 32.35%
Period: Jun 29, 2010 – Sep 24, 2025 (+11,356.36%)
Simple Annual Growth Rate: +758.5%
Tesla (Daily)
Trades: 56
Win Rate: 35.71%
Period: Jun 29, 2010 – Sep 24, 2025 (+3,166.64%)
Simple Annual Growth Rate: +211.5%
BTC/USDT (Daily)
Trades: 44
Win Rate: 31.82%
Period: Sep 30, 2017 – Sep 24, 2025 (+2,592.23%)
Simple Annual Growth Rate: +324.8%
SPY (Daily)
Trades: 81
Win Rate: 37.04%
Period: Jan 23, 1993 – Sep 24, 2025 (+476.90%)
Simple Annual Growth Rate: +14.3%
XAU/USD (Daily)
Trades: 216
Win Rate: 32.87%
Period: Jan 6, 1833 – Sep 24, 2025 (+5,241.73%)
Simple Annual Growth Rate: +27.1%
SPX (Daily)
Trades: 217
Win Rate: 38.25%
Period: Feb 1, 1871 – Sep 24, 2025 (+16,791.02%)
Simple Annual Growth Rate: +108.1%
Conclusion
With the “ Hosoda’s Clouds ” strategy, I aim to showcase the potential of technical analysis to generate consistent profits in trending markets, challenging recent doubts about its effectiveness. My goal is for this system to serve as both a practical tool for traders and a source of inspiration for the trading community I deeply respect. I hope it encourages the creation of new strategies, fosters creativity in technical analysis, and empowers traders to approach the markets with confidence and discipline.
Real 10Y Yield (DGS10 - T10YIE)The Real 10Y Yield (DGS10 – T10YIE) indicator computes the inflation-adjusted U.S. 10-year Treasury yield by subtracting the 10-year breakeven inflation rate (T10YIE) from the nominal 10-year Treasury yield (DGS10), both sourced directly from FRED. By filtering out inflation expectations, this script reveals the true, real borrowing cost over a 10-year horizon—one of the most reliable gauges of overall risk sentiment and capital–market health.
How It Works
Data Inputs
• DGS10 (Nominal 10-Year Treasury Yield)
• T10YIE (10-Year Breakeven Inflation Rate)
Both series are fetched on a daily timeframe via request.security from FRED.
Real Yield Calculation
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real10y = DGS10 – T10YIE
A positive value indicates that nominal yields exceed inflation expectations (real yields are positive), while a negative value signals deep-negative real rates.
Thresholds & Coloring
• Bullish Zone: Real yield < –0.1 %
• Bearish Zone: Real yield > +0.1 %
The background turns green when real yields drop below –0.1 %, reflecting an ultra-accommodative environment that historically aligns with risk-on rallies. It turns red when real yields exceed +0.1 %, indicating expensive real borrowing costs and a potential shift toward risk-off.
Alerts
• Deep-Negative Real Yields (Bullish): Triggers when real yield < –0.1 %
• High Real Yields (Bearish): Triggers when real yield > +0.1 %
Why It’s Powerful
Forward-Looking Sentiment Gauge
Real yields incorporate both market-implied inflation and nominal rates, making them a leading indicator for risk appetite, equity flows, and crypto demand.
Clear, Actionable Zones
The –0.1 % / +0.1 % thresholds cleanly delineate structurally bullish vs. bearish regimes, removing noise and false signals common in nominal-only yield studies.
Macro & Cross-Asset Confluence
Combine with equity indices, dollar strength (DXY), or credit spreads for a fully contextual macro view. When real yields break deeper negative alongside weakening dollar, it often precedes stretch in risk assets.
Automatic Alerts
Never miss regime shifts—alerts notify you the moment real yields breach key zones, so you can align your strategy with prevailing macro momentum.
How to Use
Add to a separate pane for unobstructed visibility.
Monitor breaks beneath –0.1 % for early “risk-on” signals in stocks, commodities, and crypto.
Watch for climbs above +0.1 % to hedge or rotate into defensive assets.
Combine with your existing trend-following or mean-reversion strategies to improve timing around major market turning points.
–––
Feel free to adjust the threshold lines to your preferred sensitivity (e.g., tighten to ±0.05 %), or overlay with moving averages to smooth out whipsaws. This script is ideal for macro traders, portfolio managers, and quantitative quants who demand a distilled, inflation-adjusted view of real rates.
True Breakout Pattern [TradingFinder] Breakout Signal Indicator🔵 Introduction
In many market conditions, what initially appears to be a decisive breakout often turns out to be nothing more than a false breakout or fake breakout. Price breaks through a key swing level or an important support and resistance zone, only to quickly return to its previous range.
These failed breakouts, which are often the result of liquidity traps or market manipulation, serve more as a warning sign of structural weakness than confirmation of a new trend.
This indicator is designed around the concept of the fake breakout.
The logic is simple but precise : when price breaks a swing level and returns to that level within a maximum of five candles, the move is considered a false breakout. At this point, a Fibonacci retracement is applied to the recent price swing to evaluate the pullback area.
If price, within ten candles after the return to the breakout level, enters the Fibonacci zone between 0.618 and 1.0, the setup becomes valid for a potential entry. This area is identified as a long entry zone, with the stop loss placed just beyond the 1.0 level and the take profit defined based on the desired risk-to-reward ratio.
By combining accurate detection of false breakouts, analysis of price reaction to swing levels, and alignment with Fibonacci retracement logic, this framework allows traders to identify opportunities often missed by others. In a market where failed breakouts are a common and recurring phenomenon, this indicator aims to transform these traps into measurable trading opportunities.
Long Setup :
Short Setup :
🔵 How to Use
This indicator operates based on the recognition of false breakouts from structural levels in the market, specifically swing levels, and combines that with Fibonacci retracement analysis.
In this strategy, trades are only considered when price returns to the broken level within a defined time window and reacts appropriately inside a predefined Fibonacci range. Depending on the direction of the initial breakout, the system outlines two scenarios for long and short setups.
🟣 Long Setup
In the long setup, price initially breaks below a support level or swing low. If the price returns to the broken level within a maximum of five candles, the move is identified as a fake breakout.
At this stage, a Fibonacci retracement is drawn from the recent high to the low. If price, within ten candles of returning to the level, moves into the 0.618 to 1.0 Fibonacci zone, the conditions for a long entry are met.
The stop loss is placed slightly below the 1.0 level, while the take profit is set based on the trader’s preferred risk-reward ratio. This setup aims to capture deeply discounted entries at low risk, aligned with smart money reversals.
🟣 Short Setup
In the short setup, the price breaks above a resistance level or swing high. If the price returns to that level within five candles, the move is again treated as a false breakout. Fibonacci is then drawn from the recent low to the high to observe the retracement area.
Should price enter the 0.618 to 1.0 Fibonacci range within ten candles of returning, a short entry is considered valid. In this case, the stop loss is placed just above the 1.0 level, and the take profit is adjusted based on the intended risk-reward target. This method allows traders to identify high-probability short setups by focusing on failed breakouts and deep pullbacks.
🔵 Settings
🟣 Logical settings
Swing period : You can set the swing detection period.
Valid After Trigger Bars : Limits how many candles after a fake breakout the entry zone remains valid.
Max Swing Back Method : It is in two modes "All" and "Custom". If it is in "All" mode, it will check all swings, and if it is in "Custom" mode, it will check the swings to the extent you determine.
Max Swing Back : You can set the number of swings that will go back for checking.
🟣 Display settings
Displaying or not displaying swings and setting the color of labels and lines.
🟣 Alert Settings
Alert False Breakout : Enables alerts for Breakout.
Message Frequency : Determines the frequency of alerts. Options include 'All' (every function call), 'Once Per Bar' (first call within the bar), and 'Once Per Bar Close' (final script execution of the real-time bar). Default is 'Once per Bar'.
Show Alert Time by Time Zone : Configures the time zone for alert messages. Default is 'UTC'.
🔵 Conclusion
A sound understanding of the false breakout phenomenon and its relationship to structural price behavior is essential for technical traders aiming to improve precision and consistency. Many poor trading decisions stem from misinterpreting failed breakouts and entering too early into weak signals.
A structured approach, grounded in the analysis of swing levels and validated through specific price action and timing rules, can turn these misleading moves into valuable trade opportunities.
This indicator, by combining fake breakout detection with time filters and Fibonacci-based retracement zones, helps traders only engage with the market when multiple confirming factors are in alignment. The result is a strategy that emphasizes probability, risk control, and clarity in decision-making, offering a solid edge in navigating today’s volatile markets.
Lyapunov Market Instability (LMI)Lyapunov Market Instability (LMI)
What is Lyapunov Market Instability?
Lyapunov Market Instability (LMI) is a revolutionary indicator that brings chaos theory from theoretical physics into practical trading. By calculating Lyapunov exponents—a measure of how rapidly nearby trajectories diverge in phase space—LMI quantifies market sensitivity to initial conditions. This isn't another oscillator or trend indicator; it's a mathematical lens that reveals whether markets are in chaotic (trending) or stable (ranging) regimes.
Inspired by the meditative color field paintings of Mark Rothko, this indicator transforms complex chaos mathematics into an intuitive visual experience. The elegant simplicity of the visualization belies the sophisticated theory underneath—just as Rothko's seemingly simple color blocks contain profound depth.
Theoretical Foundation (Chaos Theory & Lyapunov Exponents)
In dynamical systems, the Lyapunov exponent (λ) measures the rate of separation of infinitesimally close trajectories:
λ > 0: System is chaotic—small changes lead to dramatically different outcomes (butterfly effect)
λ < 0: System is stable—trajectories converge, perturbations die out
λ ≈ 0: Edge of chaos—transition between regimes
Phase Space Reconstruction
Using Takens' embedding theorem , we reconstruct market dynamics in higher dimensions:
Time-delay embedding: Create vectors from price at different lags
Nearest neighbor search: Find historically similar market states
Trajectory evolution: Track how these similar states diverged over time
Divergence rate: Calculate average exponential separation
Market Application
Chaotic markets (λ > threshold): Strong trends emerge, momentum dominates, use breakout strategies
Stable markets (λ < threshold): Mean reversion dominates, fade extremes, range-bound strategies work
Transition zones: Market regime about to change, reduce position size, wait for confirmation
How LMI Works
1. Phase Space Construction
Each point in time is embedded as a vector using historical prices at specific delays (τ). This reveals the market's hidden attractor structure.
2. Lyapunov Calculation
For each current state, we:
- Find similar historical states within epsilon (ε) distance
- Track how these initially similar states evolved
- Measure exponential divergence rate
- Average across multiple trajectories for robustness
3. Signal Generation
Chaos signals: When λ crosses above threshold, market enters trending regime
Stability signals: When λ crosses below threshold, market enters ranging regime
Divergence detection: Price/Lyapunov divergences signal potential reversals
4. Rothko Visualization
Color fields: Background zones represent market states with Rothko-inspired palettes
Glowing line: Lyapunov exponent with intensity reflecting market state
Minimalist design: Focus on essential information without clutter
Inputs:
📐 Lyapunov Parameters
Embedding Dimension (default: 3)
Dimensions for phase space reconstruction
2-3: Simple dynamics (crypto/forex) - captures basic momentum patterns
4-5: Complex dynamics (stocks/indices) - captures intricate market structures
Higher dimensions need exponentially more data but reveal deeper patterns
Time Delay τ (default: 1)
Lag between phase space coordinates
1: High-frequency (1m-15m charts) - captures rapid market shifts
2-3: Medium frequency (1H-4H) - balances noise and signal
4-5: Low frequency (Daily+) - focuses on major regime changes
Match to your timeframe's natural cycle
Initial Separation ε (default: 0.001)
Neighborhood size for finding similar states
0.0001-0.0005: Highly liquid markets (major forex pairs)
0.0005-0.002: Normal markets (large-cap stocks)
0.002-0.01: Volatile markets (crypto, small-caps)
Smaller = more sensitive to chaos onset
Evolution Steps (default: 10)
How far to track trajectory divergence
5-10: Fast signals for scalping - quick regime detection
10-20: Balanced for day trading - reliable signals
20-30: Slow signals for swing trading - major regime shifts only
Nearest Neighbors (default: 5)
Phase space points for averaging
3-4: Noisy/fast markets - adapts quickly
5-6: Balanced (recommended) - smooth yet responsive
7-10: Smooth/slow markets - very stable signals
📊 Signal Parameters
Chaos Threshold (default: 0.05)
Lyapunov value above which market is chaotic
0.01-0.03: Sensitive - more chaos signals, earlier detection
0.05: Balanced - optimal for most markets
0.1-0.2: Conservative - only strong trends trigger
Stability Threshold (default: -0.05)
Lyapunov value below which market is stable
-0.01 to -0.03: Sensitive - quick stability detection
-0.05: Balanced - reliable ranging signals
-0.1 to -0.2: Conservative - only deep stability
Signal Smoothing (default: 3)
EMA period for noise reduction
1-2: Raw signals for experienced traders
3-5: Balanced - recommended for most
6-10: Very smooth for position traders
🎨 Rothko Visualization
Rothko Classic: Deep reds for chaos, midnight blues for stability
Orange/Red: Warm sunset tones throughout
Blue/Black: Cool, meditative ocean depths
Purple/Grey: Subtle, sophisticated palette
Visual Options:
Market Zones : Background fields showing regime areas
Transitions: Arrows marking regime changes
Divergences: Labels for price/Lyapunov divergences
Dashboard: Real-time state and trading signals
Guide: Educational panel explaining the theory
Visual Logic & Interpretation
Main Elements
Lyapunov Line: The heart of the indicator
Above chaos threshold: Market is trending, follow momentum
Below stability threshold: Market is ranging, fade extremes
Between thresholds: Transition zone, reduce risk
Background Zones: Rothko-inspired color fields
Red zone: Chaotic regime (trending)
Gray zone: Transition (uncertain)
Blue zone: Stable regime (ranging)
Transition Markers:
Up triangle: Entering chaos - start trend following
Down triangle: Entering stability - start mean reversion
Divergence Signals:
Bullish: Price makes low but Lyapunov rising (stability breaking down)
Bearish: Price makes high but Lyapunov falling (chaos dissipating)
Dashboard Information
Market State: Current regime (Chaotic/Stable/Transitioning)
Trading Bias: Specific strategy recommendation
Lyapunov λ: Raw value for precision
Signal Strength: Confidence in current regime
Last Change: Bars since last regime shift
Action: Clear trading directive
Trading Strategies
In Chaotic Regime (λ > threshold)
Follow trends aggressively: Breakouts have high success rate
Use momentum strategies: Moving average crossovers work well
Wider stops: Expect larger swings
Pyramid into winners: Trends tend to persist
In Stable Regime (λ < threshold)
Fade extremes: Mean reversion dominates
Use oscillators: RSI, Stochastic work well
Tighter stops: Smaller expected moves
Scale out at targets: Trends don't persist
In Transition Zone
Reduce position size: Uncertainty is high
Wait for confirmation: Let regime establish
Use options: Volatility strategies may work
Monitor closely: Quick changes possible
Advanced Techniques
- Multi-Timeframe Analysis
- Higher timeframe LMI for regime context
- Lower timeframe for entry timing
- Alignment = highest probability trades
- Divergence Trading
- Most powerful at regime boundaries
- Combine with support/resistance
- Use for early reversal detection
- Volatility Correlation
- Chaos often precedes volatility expansion
- Stability often precedes volatility contraction
- Use for options strategies
Originality & Innovation
LMI represents a genuine breakthrough in applying chaos theory to markets:
True Lyapunov Calculation: Not a simplified proxy but actual phase space reconstruction and divergence measurement
Rothko Aesthetic: Transforms complex math into meditative visual experience
Regime Detection: Identifies market state changes before price makes them obvious
Practical Application: Clear, actionable signals from theoretical physics
This is not a combination of existing indicators or a visual makeover of standard tools. It's a fundamental rethinking of how we measure and visualize market dynamics.
Best Practices
Start with defaults: Parameters are optimized for broad market conditions
Match to your timeframe: Adjust tau and evolution steps
Confirm with price action: LMI shows regime, not direction
Use appropriate strategies: Chaos = trend, Stability = reversion
Respect transitions: Reduce risk during regime changes
Alerts Available
Chaos Entry: Market entering chaotic regime - prepare for trends
Stability Entry: Market entering stable regime - prepare for ranges
Bullish Divergence: Potential bottom forming
Bearish Divergence: Potential top forming
Chart Information
Script Name: Lyapunov Market Instability (LMI) Recommended Use: All markets, all timeframes Best Performance: Liquid markets with clear regimes
Academic References
Takens, F. (1981). "Detecting strange attractors in turbulence"
Wolf, A. et al. (1985). "Determining Lyapunov exponents from a time series"
Rosenstein, M. et al. (1993). "A practical method for calculating largest Lyapunov exponents"
Note: After completing this indicator, I discovered @loxx's 2022 "Lyapunov Hodrick-Prescott Oscillator w/ DSL". While both explore Lyapunov exponents, they represent independent implementations with different methodologies and applications. This indicator uses phase space reconstruction for regime detection, while his combines Lyapunov concepts with HP filtering.
Disclaimer
This indicator is for research and educational purposes only. It does not constitute financial advice or provide direct buy/sell signals. Chaos theory reveals market character, not future prices. Always use proper risk management and combine with your own analysis. Past performance does not guarantee future results.
See markets through the lens of chaos. Trade the regime, not the noise.
Bringing theoretical physics to practical trading through the meditative aesthetics of Mark Rothko
Trade with insight. Trade with anticipation.
— Dskyz , for DAFE Trading Systems
Divergence Macro Sentiment Indicator (DMSI)The Divergence Macro Sentiment Indicator (DMSI)
Think of DMSI as your daily “mood ring” for the markets. It boils down the tug-of-war between growth assets (S&P 500, copper, oil) and safe havens (gold, VIX) into one clear histogram—so you instantly know if the bulls have broad backing or are charging ahead with one foot tied behind.
🔍 What You’re Seeing
Green bars (above zero): Risk-on conviction.
Equities and commodities are rallying while gold and volatility retreat.
Red bars (below zero): Risk-off caution.
Gold or VIX are climbing even as stocks rise—or stocks aren’t fully joined by oil/copper.
Zero line: The line in the sand between “full-steam ahead” and “proceed with care.”
📈 How to Read It
Cross-Zero Signals
Bullish trigger: DMSI flips up through zero after a red stretch → fresh long entries.
Bearish trigger: DMSI tumbles below zero from green territory → tighten stops or go defensive.
Divergence Warnings
If SPX makes new highs but DMSI is rolling over (lower green bars or red), that’s your early red flag—rallies may fizzle.
Strength Confirmation
On pullbacks, only buy dips when DMSI ≥ 0. When DMSI is deeply positive, you can be more aggressive on position size or add leverage.
💡 Trade Guidance & Use Cases
Trend Filter: Only take your S&P or sector-ETF long setups when DMSI is non-negative—avoids hollow rallies.
Macro Pair Trades:
Deep red DMSI: go long gold or gold miners (GLD, GDX).
Strong green DMSI: lean into cyclicals, industrials, even energy names.
Risk Management:
Scale out as DMSI fades into negative territory mid-trade.
Scale in or add to winners when it stays bullish.
Swing Confirmation: Overlay on any oscillator or price-pattern system—accept signals only when the macro tide is flowing in your favour.
🚀 Why It Works
Markets don’t move in a vacuum. When stocks rally but the “real-economy” metals and volatility aren’t cooperating, something’s off under the hood. DMSI catches those cross-asset cracks before price alone can—and gives you an early warning system for smarter entries, tighter risk, and bigger gains when the macro trend really kicks in.
Price Action Dynamics Oscillator (PADO)1 minute ago
Price Action Dynamics Oscillator (PADO)
Indicator Overview and Technical Deep Dive
Concept and Philosophy
The Price Action Dynamics Oscillator (PADO) is a sophisticated technical analysis tool designed to provide multi-dimensional insights into market behavior by decomposing price action into manipulation and distribution metrics. The indicator goes beyond traditional momentum or trend indicators by introducing a nuanced approach to understanding market microstructure.
Key Architectural Components
1. Timeframe and Depth Selection
Pivot Depth Options:
Short Term (Length: 12 periods)
Intermediate Term (Length: 20 periods)
Long Term (Length: 100 periods)
This flexible configuration allows traders to adapt the indicator's sensitivity to different market conditions and trading styles.
2. Core Calculation Methodology
Manipulation Metrics
Calculates manipulation differently for green (bullish) and red (bearish) candles
Normalized against Average True Range (ATR) for consistent comparison across different volatility environments
Green Candle Manipulation: (Open - Low) / ATR
Red Candle Manipulation: (High - Open) / ATR
Distribution Metrics
Measures the directional strength and potential momentum shift
Green Candle Distribution: (Close - Open)
Red Candle Distribution: (Open - Close)
3. Normalization and Smoothing
Uses Simple Moving Average (SMA) for smoothing
Dynamic length calculation based on price range distance
Ensures minimum SMA length of 2 to prevent calculation errors
Unique Features
Visualization Toggles
Traders can selectively display:
Manipulation data
Distribution data
Long-term reference lines
Valuation metrics
Strategy signals
Valuation Comparative Analysis
Compares current manipulation and distribution metrics to 1000-bar long-term averages
Color-coded visualization for quick interpretation
Blue: Manipulation above average
Purple: Manipulation below average
Orange: Distribution above average
Yellow: Distribution below average
Strategy Deployment
Generates a composite strategy signal by comparing manipulation and distribution valuations
Uses Exponential Moving Average (EMA) for smoother signal generation
Incorporates volatility bands for context-aware signal interpretation
Quadrant Analysis
Classifies market state into four quadrants based on manipulation and distribution valuations:
Q1: Low Manipulation, High Distribution
Q2: High Manipulation, High Distribution
Q3: Low Manipulation, Low Distribution
Q4: High Manipulation, Low Distribution
Each quadrant is color-coded to provide visual market state representation.
Warning Signals
Manipulation Warning: When strategy crosses below low volatility band
Distribution Warning: When strategy crosses above high volatility band
Visual Indicators
Bar coloration based on strategy momentum
Multiple color states representing different market dynamics
Recommended Use Cases
Intraday and swing trading
Multi-timeframe market analysis
Volatility and momentum assessment
Trend reversal and continuation identification
Potential Limitations
Complexity might require significant trader education
Performance can vary across different market conditions
Requires careful parameter optimization
Recommended Settings
Best used on liquid markets with clear price action
Ideal for:
Forex
Futures
Large-cap stocks
Cryptocurrency pairs
Customization and Optimization
Traders should:
Backtest across multiple assets
Adjust timeframe settings
Calibrate visualization toggles
Use in conjunction with other technical indicators
Licensing
Mozilla Public License 2.0
Open-source and modification-friendly
Conclusion
The PADO represents an advanced approach to market analysis, blending traditional technical analysis with innovative metrics for deeper market understanding.
PADO Quadrant Color Analysis: Deep Dive
Quadrant Color Scheme Breakdown
Quadrant 1: Lime Green Background (RGB: 0, 255, 21, 90)
Condition: val_manip < 1 AND val_distr > 1
Market Interpretation:
Low Manipulation Pressure
High Distribution Activity
Potential Scenario:
Smart money might be gradually distributing positions
Trading Implications:
Caution for current trend followers
Potential preparation for trend change
Increased probability of consolidation or reversal
Quadrant 2: Bright Blue Background (RGB: 0, 191, 255, 90)
Condition: val_manip > 1 AND val_distr > 1
Market Interpretation:
High Manipulation Pressure
High Distribution Activity
Potential Scenario:
Strong institutional involvement
Potential market transition phase
Significant volume and momentum
Trading Implications:
High volatility expected
Increased market uncertainty
Potential for sharp price movements
Requires careful risk management
Quadrant 3: Light Gray Background (RGB: 252, 252, 252, 90)
Condition: val_manip < 1 AND val_distr < 1
Market Interpretation:
Low Manipulation Pressure
Low Distribution Activity
Potential Scenario:
Market consolidation
Reduced institutional activity
Potential low-volatility period
Trading Implications:
Range-bound market
Reduced trading opportunities
Potential setup for future breakout
Ideal for mean reversion strategies
Quadrant 4: Light Yellow Background (Hex: #f6ff0019)
Condition: val_manip > 1 AND val_distr < 1
Market Interpretation:
High Manipulation Pressure
Low Distribution Activity
Potential Scenario:
Accumulation of positions
Trading Implications:
Increased probability of directional move soon
Color Psychology and Technical Significance
Color Selection Rationale
Lime Green (Q1): Represents potential growth and transition
Bright Blue (Q2): Signifies high energy and institutional activity
Light Gray (Q3): Indicates neutrality and consolidation
Transparent Green (Q4): Suggests emerging trend potential
Advanced Interpretation Guidelines
Color Transition Analysis
Observe how the quadrant colors change
Rapid color shifts might indicate:
Market regime changes
Shifts in institutional sentiment
Potential trend acceleration or reversal
Technical Implementation Notes
Calculation Snippet
pinescriptCopyq1 = (val_manip < 1) and (val_distr > 1)
q2 = (val_manip > 1) and (val_distr > 1)
q3 = (val_manip < 1) and (val_distr < 1)
q4 = (val_manip > 1) and (val_distr < 1)
bgcolor(q1 ? color.rgb(0, 255, 21, 90):
q2 ? color.rgb(0, 191, 255, 90):
q3 ? color.rgb(252, 252, 252, 90):
q4 ? #f6ff0019:na)
Alpha Channel (Transparency)
90 and 0x19 values ensure background color doesn't overwhelm chart
Allows underlying price action to remain visible
Subtle visual cue without significant chart obstruction
Practical Trading Recommendations
Never Trade Solely on Quadrant Colors
Use as a complementary analysis tool
Combine with other technical and fundamental indicators
Timeframe Considerations
Validate quadrant signals across multiple timeframes
Longer timeframes provide more reliable signals
Risk Management
Set appropriate stop-loss levels
Use position sizing strategies
Be prepared for false signals
Recommended Workflow
Identify current quadrant
Assess overall market context
Confirm with other indicators
Execute with proper risk management
Goertzel Cycle Composite Wave [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Cycle Composite Wave indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
*** To decrease the load time of this indicator, only XX many bars back will render to the chart. You can control this value with the setting "Number of Bars to Render". This doesn't have anything to do with repainting or the indicator being endpointed***
█ Brief Overview of the Goertzel Cycle Composite Wave
The Goertzel Cycle Composite Wave is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The Goertzel Cycle Composite Wave is considered a non-repainting and endpointed indicator. This means that once a value has been calculated for a specific bar, that value will not change in subsequent bars, and the indicator is designed to have a clear start and end point. This is an important characteristic for indicators used in technical analysis, as it allows traders to make informed decisions based on historical data without the risk of hindsight bias or future changes in the indicator's values. This means traders can use this indicator trading purposes.
The repainting version of this indicator with forecasting, cycle selection/elimination options, and data output table can be found here:
Goertzel Browser
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the cycles. The color of the lines indicates whether the wave is increasing or decreasing.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast: These inputs define the window size for the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Cycle Composite Wave Code
The Goertzel Cycle Composite Wave code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Cycle Composite Wave function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past sizes (WindowSizePast), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Cycle Composite Wave algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Cycle Composite Wave code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Cycle Composite Wave code calculates the waveform of the significant cycles for specified time windows. The windows are defined by the WindowSizePast parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in a matrix:
The calculated waveforms for the cycle is stored in the matrix - goeWorkPast. This matrix holds the waveforms for the specified time windows. Each row in the matrix represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Cycle Composite Wave function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Cycle Composite Wave code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Cycle Composite Wave's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for specified time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast:
The WindowSizePast is updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
The matrix goeWorkPast is initialized to store the Goertzel results for specified time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for waveforms:
The goertzel array is initialized to store the endpoint Goertzel.
Calculating composite waveform (goertzel array):
The composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Drawing composite waveform (pvlines):
The composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms and visualizes them on the chart using colored lines.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
Limited applicability:
The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Cycle Composite Wave indicator can be interpreted by analyzing the plotted lines. The indicator plots two lines: composite waves. The composite wave represents the composite wave of the price data.
The composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend.
Interpreting the Goertzel Cycle Composite Wave indicator involves identifying the trend of the composite wave lines and matching them with the corresponding bullish or bearish color.
█ Conclusion
The Goertzel Cycle Composite Wave indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Cycle Composite Wave indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Cycle Composite Wave indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
1. The first term represents the deviation of the data from the trend.
2. The second term represents the smoothness of the trend.
3. λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
Goertzel Browser [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Browser indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
█ Brief Overview of the Goertzel Browser
The Goertzel Browser is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
3. Project the composite wave into the future, providing a potential roadmap for upcoming price movements.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the past and dotted lines for the future projections. The color of the lines indicates whether the wave is increasing or decreasing.
5. Displaying cycle information: The indicator provides a table that displays detailed information about the detected cycles, including their rank, period, Bartel's test results, amplitude, and phase.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements and their potential future trajectory, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast and WindowSizeFuture: These inputs define the window size for past and future projections of the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
UseCycleList: This boolean input determines whether a user-defined list of cycles should be used for constructing the composite wave. If set to false, the top N cycles will be used.
Cycle1, Cycle2, Cycle3, Cycle4, and Cycle5: These inputs define the user-defined list of cycles when 'UseCycleList' is set to true. If using a user-defined list, each of these inputs represents the period of a specific cycle to include in the composite wave.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Browser Code
The Goertzel Browser code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Browser function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past and future window sizes (WindowSizePast, WindowSizeFuture), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, goeWorkFuture, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Browser algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Browser code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Browser code calculates the waveform of the significant cycles for both past and future time windows. The past and future windows are defined by the WindowSizePast and WindowSizeFuture parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in matrices:
The calculated waveforms for each cycle are stored in two matrices - goeWorkPast and goeWorkFuture. These matrices hold the waveforms for the past and future time windows, respectively. Each row in the matrices represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Browser function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Browser code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Browser's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for both past and future time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast and WindowSizeFuture:
The WindowSizePast and WindowSizeFuture are updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
Two matrices, goeWorkPast and goeWorkFuture, are initialized to store the Goertzel results for past and future time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for past and future waveforms:
Three arrays, epgoertzel, goertzel, and goertzelFuture, are initialized to store the endpoint Goertzel, non-endpoint Goertzel, and future Goertzel projections, respectively.
Calculating composite waveform for past bars (goertzel array):
The past composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Calculating composite waveform for future bars (goertzelFuture array):
The future composite waveform is calculated in a similar way as the past composite waveform.
Drawing past composite waveform (pvlines):
The past composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
Drawing future composite waveform (fvlines):
The future composite waveform is drawn on the chart using dotted lines. The color of the lines is determined by the direction of the waveform (fuchsia for upward, yellow for downward).
Displaying cycle information in a table (table3):
A table is created to display the cycle information, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
Filling the table with cycle information:
The indicator iterates through the detected cycles and retrieves the relevant information (period, amplitude, phase, and Bartel value) from the corresponding arrays. It then fills the table with this information, displaying the values up to six decimal places.
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms for both past and future time windows and visualizes them on the chart using colored lines. Additionally, it displays detailed cycle information in a table, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles and potential future impact. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
No guarantee of future performance: While the script can provide insights into past cycles and potential future trends, it is important to remember that past performance does not guarantee future results. Market conditions can change, and relying solely on the script's predictions without considering other factors may lead to poor trading decisions.
Limited applicability: The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Browser indicator can be interpreted by analyzing the plotted lines and the table presented alongside them. The indicator plots two lines: past and future composite waves. The past composite wave represents the composite wave of the past price data, and the future composite wave represents the projected composite wave for the next period.
The past composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend. On the other hand, the future composite wave line is a dotted line with fuchsia indicating a bullish trend and yellow indicating a bearish trend.
The table presented alongside the indicator shows the top cycles with their corresponding rank, period, Bartels, amplitude or cycle strength, and phase. The amplitude is a measure of the strength of the cycle, while the phase is the position of the cycle within the data series.
Interpreting the Goertzel Browser indicator involves identifying the trend of the past and future composite wave lines and matching them with the corresponding bullish or bearish color. Additionally, traders can identify the top cycles with the highest amplitude or cycle strength and utilize them in conjunction with other technical indicators and fundamental analysis for trading decisions.
This indicator is considered a repainting indicator because the value of the indicator is calculated based on the past price data. As new price data becomes available, the indicator's value is recalculated, potentially causing the indicator's past values to change. This can create a false impression of the indicator's performance, as it may appear to have provided a profitable trading signal in the past when, in fact, that signal did not exist at the time.
The Goertzel indicator is also non-endpointed, meaning that it is not calculated up to the current bar or candle. Instead, it uses a fixed amount of historical data to calculate its values, which can make it difficult to use for real-time trading decisions. For example, if the indicator uses 100 bars of historical data to make its calculations, it cannot provide a signal until the current bar has closed and become part of the historical data. This can result in missed trading opportunities or delayed signals.
█ Conclusion
The Goertzel Browser indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Browser indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Browser indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
The first term represents the deviation of the data from the trend.
The second term represents the smoothness of the trend.
λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
Per Volume Price ImpactLiquidity, Information and Market Timing
* Market Liquidity
The term liquidity can refer to many things in finance. In this article, we will limit the scope of discussion to the market’s ability to transact without incurring a significant increase in volatility.
As we know, liquidity and volatility have an inversed relationship — the more ample the liquidity, the lower the volatility (attributed to transaction cost, price movement and, so on). With this understanding, we can say large movements in the market are driven by low liquidity. This does not seem to make sense because the markets are huge, how can it possibly be illiquid? Now, this has to do with how the market operates and how exchanges occur (This topic concerns the area of market microstructure).
* Order Book & the Trading Process
So how does a transaction actually occur in the market? Let’s assume we open a position with a market order. In this case, you will get the price on your quote board if there are enough units of assets people are willing to sell at that price. If there are not enough units, you will buy from the second-best price and so on until your order is filled. Now in the second case, as the order is being filled, the change in price is recorded. Therefore, if someone wishes to move the market, theoretically, they just need to buy up or sell up but it is problematic to do so.
Here is why:
while dry up the liquidity can make huge moves, it is inefficient to do so.
it takes a lot of money to do that
your position will be exposed, someone more resourceful than you may go against you and that is a huge risk
market manipulation charges
when you open a position, the entry price of the position is essentially a VWAP (volume-weighted average price). If you attempt to move the market and open a buy position at the same time, you will have a higher VWAP, eating into your own profit.
I think these reasons are sufficient in establishing why opening a position and drying up liquidity to profit is a dumb idea. But of course, the institutions are not stupid, the alternative is to enter your position first then move the market.
To measure liquidity one of the tools people use is the order book. It can offer an overview of the sentiment (by looking at the orders and changes in volume) and how people are positioned (if the broker offers such data). In my opinion, open interest is a much better tool than order as it records the transactions that have occurred, hence less prone to manipulations (google: “Navinder Singh Sarao”, the trader who used fake orders to manipulate algorithms to crash the market).
But to quantify the order book is so much work as well (there are ways, just difficult), what we can do is to make things simpler.
* Quantify Market Impact
We know price and volume reflect information, while the past technical information has no predictive power per semi-strong form of EMH, empirical studies have often tested this theory over a longer time horizon. In our case, precisely due to the mechanism of exchange and human behavior (The lack of incentive to move the market right away) we can, in the very short term (often intraday), foresee if the market is going to move or not. Back to the very definition of liquidity being the ability to transact without moving the market significantly, we can take this definition and quantify it with this formula:
Market Impact = (High — Low) / Volume
Why specifically “high — low”, because that’s the complete information in that moment and it is corresponding to the volume. A little crude but it is the simplest form.
A few things to take note of here:
We can only know the complete picture once the candle is complete. This is fine in most markets because it takes time to gather money and orders.
We often see high liquidity during certain time of the day, for example, when the market opens and so on. As a result, we need to take some scientific approaches to transform the data.
Now, this looks much better. To interpret this graph, the lower the value, the lower the market impact, the deeper the liquidity.
* Generate Tradable Insights
To generate trade ideas isn’t a difficult task, we all know the RSI, MOM, STOC, etc. all the indicators attempt to draw boundaries, and we can do the same but we need to be a little more advanced and critical.
step 1: we first need to normalize the data. To do that we will take the log of the values to make the skewed distribution normal. The result isn’t ideal if you zoom out but I think this is decent enough to work with. Here is
This is still not a stationary time series, but it looks stable enough and it mean-reverts. So we turn to our lovely standard deviation bands for help.
Step 2: Because this is not a stationary process (visually, you can test it statistically if you wish), we cannot just take sample mean and SD and also because we want to show off our data skills, so we turn to move averages and regressions. I’m going to use moving regression here because I think it is better (mean can be distorted by large values by a larger margin and it lags)
I’m using the moving regression band on TradingView and 1.5 SD here for convenience, you can try to optimize the parameters with codes or other regression models if you wish. But I think it is more important to understand the rationale here.
This step is essentially trying to figure out the anomalies in liquidity so that we can see when there is deep liquidity. This is also why choosing the parameter is crucial because you are essentially approximating how much informed trading is taking place (This is a concept in market microstructure for brokerages to set their spreads but it is not a good tool in a liquid market). By setting the level at 1.5 we are assuming about 86% of the time the market is in what we consider a normal liquid state. (again it is arbitrary, but based on the 68–95–99.7 rule of normal distribution). The rest of the time will be either low or high liquidity, When liquidity is deep, it perhaps, signals institutional money is pouring into the market and big moves may follow.
* Conclusion
There you have it, how to enter the market with the big bucks. But do take note there are plenty of assumptions and a lot to improve on here.
Multi-timeframe Harmonic PatternsHello friends. In recent months I have been busy with my academic research and haven't had much time to publish new scripts. To fill the gap of these months, I decided to publish the indicator Multi-timeframe Harmonic Patterns . Harmonic technical chart patterns can predict the next price trend and provide traders with clues to the price direction, which is one of the indicators widely used by professional traders.
(1) Indicator description
This indicator is built on ZigZag Multi Time Frame with Fibonacci Retracement@LonesomeTheBlue . Thanks to LonesomeTheBlue for contributing the awesome indicator
The indicator supports 6 different timeframes , and 25 different harmonic patterns
This indicator supports indicating key indicator prices: entry price, stop loss price, and two take profit prices
(2) Key parameters
timeframe resolution: The timeframe of the harmonic pattern
pivot high/low source: Calculation method of high/low pivot points
timeframe pivot period: Minimum period of high/low pivot points
delay for confirmations: Wait for N candles to confirm the chart pattern
bullish/bearish colors: Bullish/bearish pattern colors
enable harmonic patterns: Enable current harmonic patterns
show harmonic patterns: Show harmonic patterns found
show trading prices of patterns: Show key prices of harmonic patterns
(3) Supported Patterns:
Gartlay
Cypher
Bat
Deepcrab
Crab
Butterfly
Shark
0-5
AB=CD
3-Drives
Anti-Gartlay
Anti-Cypher
Anti-Bat
Anti-Crab
Anti-Butterfly
Anti-Shark
Black-Swan
White-Swan
Descending-Triangle
Ascending-Triangle
Symmetrical-Triangle
Headers&Shoulders
Inverse-Headers&Shoulders
Double-Top
Double-Bottom
————————————————————————————————————————
各位朋友大家好。最近几个月我忙于自己的学术研究没有过多时间更新脚本。为弥补这几个月的空缺，我决定发布该 多时间周期的谐波指标 。谐波技术图表形态在一定程度上可以预测下一个价格走势，为交易者提供价格方向的线索，是广大专业交易人员广泛使用的指标之一。
(1) 指标说明
该指标建立于 ZigZag Multi Time Frame with Fibonacci Retracement@LonesomeTheBlue ，感谢LonesomeTheBlue贡献的出色指标
该指标支持 6种不同的时间周期 ，以及 25种不同的谐波形态
该指标支持指示关键的指标价格：入场价格、止损价格、以及两种止盈价格
(2) 关键参数
timeframe resolution: 谐波形态的时间周期
pivot high/low source: 高/低枢纽点的计算方式
timeframe pivot period: 高/低枢纽点的最小周期
delay for confirmations: 等待N个蜡烛以确认图表形态
bullish/bearish colors: 看涨/看跌的形态颜色
enable harmonic patterns: 使能当前的谐波形态
show harmonic patterns: 显示被发现的谐波形态
show trading prices of patterns: 显示谐波形态的关键价格
(3) 支持形态:
Gartlay
Cypher
Bat
Deepcrab
Crab
Butterfly
Shark
0-5
AB=CD
3-Drives
Anti-Gartlay
Anti-Cypher
Anti-Bat
Anti-Crab
Anti-Butterfly
Anti-Shark
Black-Swan
White-Swan
Descending-Triangle
Ascending-Triangle
Symmetrical-Triangle
Headers&Shoulders
Inverse-Headers&Shoulders
Double-Top
Double-Bottom
Smart Money Support/Resistance — LiteSmart Money Support/Resistance — Lite
Overview & Methodology
This indicator identifies support and resistance as zones derived from concentrated buying and selling pressure, rather than relying solely on traditional swing highs/lows. Its design focuses on transparency: how data is sourced, how zones are computed, and how the on‑chart display should be interpreted.
Lower‑Timeframe (LTF) Data
The script requests Up Volume, Down Volume, and Volume Delta from a lower timeframe to expose intrabar order‑flow structure that the chart’s native timeframe cannot show. In practical terms, this lets you see where buyers or sellers briefly dominated inside the body of a higher‑timeframe bar.
bool use_custom_tf_input = input.bool(true, title="Use custom lower timeframe", tooltip="Override the automatically chosen lower timeframe for volume calculations.", group=grpVolume)
string custom_tf_input = input. Timeframe("1", title="Lower timeframe", tooltip="Lower timeframe used for up/down volume calculations (default 5 seconds).", group=grpVolume)
import TradingView/ta/10 as tvta
resolve_lower_tf(useCustom, customTF) =>
useCustom ? customTF :
timeframe.isseconds ? "1S" :
timeframe.isintraday ? "1" :
timeframe.isdaily ? "5" : "60"
get_up_down_volume(lowerTf) =>
= tvta.requestUpAndDownVolume(lowerTf)
var float upVolume = na
var float downVolume = na
var float deltaVolume = na
string lower_tf = resolve_lower_tf(use_custom_tf_input, custom_tf_input)
= get_up_down_volume(lower_tf)
upVolume := u_tmp
downVolume := d_tmp
deltaVolume := dl_tmp
• Data source: TradingView’s ta.requestUpAndDownVolume(lowerTf) via the official TA library.
• Plan capabilities: higher‑tier subscriptions unlock seconds‑based charts and allow more historical bars per chart. This expands both the temporal depth of LTF data and the precision of short‑horizon analysis, while base tiers provide minute‑level data suitable for day/short‑swing studies.
• Coverage clarity: a small on‑chart Coverage Panel reports the active lower timeframe, the number of bars covered, and the latest computed support/resistance ranges so you always know the bounds of valid LTF input.
Core Method
1) Data acquisition (LTF)
The script retrieves three series from the chosen lower timeframe:
– Up Volume (buyers)
– Down Volume (sellers)
– Delta (Up – Down)
2) Rolling window & extrema
Over a user‑defined lookback (Global Volume Period), the algorithm builds rolling arrays of completed bars and scans for extrema:
– Buyers_max / Buyers_min from Up Volume
– Sellers_max / Sellers_min from Down Volume
Only completed bars are considered; the current bar is excluded for stability.
3) Price mapping
The extrema are mapped back to their source candles to obtain price bounds:
– For “maximum” roles the algorithm uses the relevant candle highs.
– For “minimum” roles it uses the relevant candle lows.
These pairs define candidate resistance (max‑based) and support (min‑based) zones or vice versa.
4) Zone construction & minimum width
To ensure practicality on all symbols, zones enforce a minimum vertical thickness of two ticks. This prevents visually invisible or overly thin ranges on instruments with tight ticks.
5) Vertical role resolution
When both max‑ and min‑based zones exist, the script compares their midpoints. If, due to local price structure, the min‑based zone sits above the max‑based zone, display roles are swapped so the higher zone is labeled Resistance and the lower zone Support. Colors/widths are updated accordingly to keep the visual legend consistent.
6) Rendering & panel
Two horizontal lines and a filled box represent each active zone. The Coverage Panel (bottom‑right by default) prints:
– Lower‑timeframe in use
– Number of bars covered by LTF data
– Current Support and Resistance ranges
If the two zones overlap, an additional “Range Market” note is shown.
Key Inputs
• Global Volume Period: shared lookback window for the extrema search.
• Lower timeframe: user‑selectable override of the automatically resolved lower timeframe.
• Visualization toggles: independent show/hide controls and colors for maximum (resistance) and minimum (support) zones.
• Coverage Panel: enable/disable the single‑cell table and its readout.
Operational Notes
• The algorithm aligns all lookups to completed bars (no peeking). Price references are shifted appropriately to avoid using the still‑forming bar in calculations.
• Second‑based lower timeframes improve granularity for scalping and very short‑term entries. Minute‑based lower timeframes provide broader coverage for intraday and short‑swing contexts.
• Use the Coverage Panel to confirm the true extent of available LTF history on your symbol/plan before drawing conclusions from very deep lookbacks.
Visual Walkthrough
A step‑by‑step image sequence accompanies this description. Each figure demonstrates how the indicator reads LTF volume, locates extrema, builds price‑mapped zones, and updates labels/colors when vertical order requires it.
Chart Interpretation
This chart illustrates two distinct perspectives of the Smart Money Support/Resistance — Lite indicator, each derived from different lookback horizons and lower-timeframe (LTF) resolutions.
1- Short-term view (43 bars, 10-second LTF)
Using the most recent 43 completed bars with 10-second intrabar data, the algorithm detects that both maximum and minimum volume extrema fall within a narrow range. The result is a clearly identified range market: resistance between 178.15–184.55 and support between 175.02–179.38.
The Coverage Panel (bottom-right) confirms the scope of valid input: the lower timeframe used, number of bars covered, and the resulting zones. This short-term scan highlights how the indicator adapts to limited data depth, flagging sideways structure where neither side dominates.
2 - Long-term view (120 bars, 30-second LTF)
Over a wider 120-bar lookback with higher-granularity 30-second data, broader supply and demand zones emerge.
– The long-term resistance zone captures the concentration of buyers and sellers at the upper boundary of recent price history.
– The long-term support zone anchors to the opposite side of the distribution, derived from maxima and minima of both buying and selling pressure.
These zones reflect deeper structural levels where market participants previously committed significant volume.
Combined Perspective
By aligning the short-term and long-term outputs, the chart shows how the indicator distinguishes immediate consolidation (range market) from more durable support and resistance levels derived from extended history. This dual resolution approach makes clear that support and resistance are not static lines but dynamic zones, dependent on both timeframe depth and the resolution of intrabar volume data.
Rapeez's BOS IndicatorIt will highlight all the BOS (Break of Structure) points on the chart with blue and red lines, making it easier to spot them without having to analyze the chart deeply. This tool is also great for identifying the overall market trend and works across all timeframes. Updates will be provided every month.
Happy charting—hope you find it helpful!
FlowScope [Hapharmonic]FlowScope: Uncover the Market's True Intent 🔬
Ever wished you could look inside the candles and see where the real action is happening? FlowScope is your microscope for the market's flow, designed to give you a powerful edge by revealing the volume distribution that price action alone can't show you.
Instead of just looking at the open, high, low, and close, FlowScope lets you dive deeper into the market's auction process. It groups candles together and builds a detailed Volume Profile for that period, showing you exactly where the trading happened and revealing the story behind the price action.
Let's explore how you can use it to gain a powerful new edge.
🧐 Core Concept: How It Works
At its heart, FlowScope does three key things:
It Groups Candles: You decide how many candles to group together. For example, setting " Group Candles " to 4 on a 5-minute chart effectively gives you a detailed 20-minute candle and profile. This helps you see the bigger picture and filter out market noise.
It Builds a Volume Profile: For each group, FlowScope analyzes the volume at every single price level. It then displays this as a horizontal histogram (we call this a "footprint" or profile). Longer bars mean more volume was traded at that price, indicating a "fair" price or an area of acceptance. Shorter bars mean price moved through quickly, indicating rejection.
It Creates a Custom "Grouped Candle": To summarize the group's overall price action, FlowScope draws a single, custom candle representing the entire group's:
Open: The open of the first candle in the group.
High: The absolute highest price reached within the group.
Low: The absolute lowest price reached within the group.
Close: The close of the last candle in the group.
This gives you a crystal-clear view of the group's net result, free from the back-and-forth noise of the individual candles inside it.
Below are some of the stunning preset color palettes you can choose from to customize your view:
🚀 How to Use: Practical Applications
FlowScope isn't just for looking pretty; it's a powerful analysis tool. Here are a few ways to integrate it into your trading:
Identify High-Volume Nodes (HVNs): Look for the longest bars in the profile. These are price levels where the market spent the most time and traded the most volume. HVNs often act as powerful "magnets" for price, becoming key areas of support and resistance.
Spot Low-Volume Nodes (LVNs): These are areas with very short bars or gaps in the profile. They represent price levels that the market moved through quickly and inefficiently. If price returns to an LVN, it's likely to move through it quickly again.
Analyze the Summary Box: This is where the real magic happens! ✨
Total Volume (Σ): The total volume for the entire group.
Buy (B) vs. Sell (S) Volume: FlowScope analyzes the lower timeframe action to estimate the buying and selling pressure that made up the total volume. Is a big red candle mostly aggressive selling, or was it just a lack of buyers? The B/S data gives you clues. A high-volume candle with nearly 50/50 buy/sell pressure might indicate absorption or a potential reversal.
Use the Grouped Candle for Clarity: Is the market in a clear uptrend, or is it just choppy? The grouped candle can give you a much clearer signal. A series of strong, green grouped candles shows much more conviction than a mix of small green and red candles.
⚙️ Settings & Customization
This is where you can truly make FlowScope your own. Let's walk through each setting.
Profile Settings
Group Candles: The number of standard chart candles you want to combine into a single FlowScope profile. A setting of 1 will analyze every single bar. A higher number gives you a broader market view. When Group Candles is set to 5, the data from the 5 individual candles are combined, and the volume is calculated accordingly.
Max Profile Boxes: This setting is more than just a number; it's a smart limit that ensures your profiles are always readable and relevant to the current market conditions.
Adaptive Sizing (The Ideal Goal): FlowScope first tries to create the perfect profile by making each volume box's height proportional to the current market volatility. It calculates an "ideal" box height based on the Average True Range ( ATR / 10 ). This is powerful because it automatically adapts: you get smaller, more detailed boxes in quiet, low-volatility markets, and larger, clearer boxes in volatile, fast-moving markets.
The Safety Cap (Your Setting): However, what if you group several candles during a massive price move? The price range could be huge! If we only used the small, ATR-based box height, you might end up with hundreds of tiny, unreadable boxes. This is where your Max Profile Boxes setting (defaulting to 50) comes in. It acts as a maximum detail cap . If the adaptive, volatility-based calculation determines that it would need more boxes than your setting (e.g., more than 50), the indicator will override it. It will then simply divide the entire price range of the group into exactly the number of boxes you specified (e.g., 50).
In short: You are setting the maximum allowable detail. FlowScope intelligently adapts the profile's granularity below that limit based on market volatility, ensuring you always get a clear and meaningful picture.
Style
Show Profile BG: A simple toggle to show or hide the faint background color behind the volume bars. Turning it off can create a cleaner look.
Color Mode: This dropdown controls how the volume profile text is colored.
Custom Gradient: This mode uses the three custom colors you select in the "Profile Colors" section to create a beautiful gradient across the profile.
Candle Color: This mode colors the profile based on whether the grouped candle was bullish (green) or bearish (red). The color will be a gradient, with the most intense color applied to the box with the highest volume; the colors of the other boxes will fade out from that point. It's a great way to see the profile's "mood" at a glance.
Profile Colors 🎨
Use Preset Palette: This is the master switch!
If checked: You can choose from 10 stunning, pre-designed color palettes from the Palette dropdown. The custom color pickers below will be disabled.
If unchecked (Default): The Palette dropdown will be disabled, and you can now choose your own three colors for the gradient.
Palette: (Only active when "Use Preset Palette" is checked) . Choose from 10 luxurious, eye-catching color schemes like "Solar Flare" or "Deep Space" to instantly change the look and feel of your chart.
Low Price / Mid Price / High Price: (Only active when "Use Preset Palette" is unchecked) . These three color pickers allow you to design your own unique gradient for the Custom Gradient color mode.
Candle Display
These settings control the custom "Grouped Candle" that summarizes the profile. When using the "Show Custom Candle" feature, you should change the chart's candlestick display to Bars for a cleaner view.
Show Custom Candle: This is the main toggle. When you check this box, the original chart candles will be hidden, and your custom FlowScope candle will be displayed instead. This custom candle is intentionally small to ensure it does not visually overlap with the volume profile boxes.
Show Body: (Only active when "Show Custom Candle" is checked) . Toggles the visibility of the candle's body.
Wick Width & Body Width: (Only active when "Show Custom Candle" is checked) . These sliders let you control the thickness of the wick and body lines to match your personal style.
Up Color / Down Color: (Only active when "Show Custom Candle" is checked) . Choose the colors for your bullish and bearish custom candles.
Experiment with the settings, find a style that works for you, and start seeing the market in a whole new light.
Happy trading! 📈😊
VSA - The Volume HUDVSA Volume HUD: Your At-a-Glance Volume Dashboard
Tired of cluttered charts with multiple indicators taking up screen space?
The VSA Volume HUD is a clean, powerful, and fully customisable Heads-Up Display that puts all the critical volume and price action data you need into one compact box, right on your chart.
Designed for traders who rely on Volume Spread Analysis (VSA), this tool helps you instantly gauge the strength, conviction, and context behind every price move as it happens.
Key Features
This indicator isn't just about showing the current volume; it provides a comprehensive, real-time analysis of the market's activity.
Real-time VSA Dashboard: A persistent on-screen table that updates with every tick, giving you instant feedback without needing to look away from the price. The HUD is fully draggable (hold Ctrl/Cmd + click and drag) to place it anywhere you like.
Essential Volume Metrics:
Current Volume: Displayed in a clean, abbreviated format (e.g., 1.25M for millions, 54.3K for thousands).
% Change (vs. Previous Bar): Instantly see if volume is expanding or contracting.
Vs Short-Term Average: Compare the current bar's volume to a moving average to spot unusual spikes.
Volume Velocity: Measures the rate of change in volume over a short period, helping you spot acceleration or deceleration in market interest.
Relative Volume (RVOL): See how the current volume compares to the average for that specific time of day, perfect for identifying abnormally high or low activity.
Price Action & Volatility Context:
Range vs. ATR: Quickly determine if the current bar's volatility is expanding or contracting compared to the recent average.
Price vs. VWAP: See how far the current price has deviated from the session's Volume-Weighted Average Price, a key level for institutional traders.
Deep Customization is Key
Tailor the HUD to perfectly match your trading style and chart aesthetic.
Display & Layout:
Compact Mode: Remove the metric labels for a sleek, minimalist view that saves screen space.
Bar Meters: Enable optional visual bars next to key metrics for a quick, graphical representation of strength.
Total Control: Toggle every single metric on or off to build the exact dashboard you need. Adjust text size, position, and background opacity with ease.
Smart Coloring & Visual Alerts:
Advanced VSA Coloring: This isn't just about up/down candles. The script intelligently colors volume based on confluence. It highlights increasing volume on a strong up-bar (bullish confirmation) or increasing volume on a down-bar (potential climax or distribution), giving you a deeper VSA context.
High Volume Highlight: Make standout bars impossible to miss! The entire HUD background can change color automatically when volume surges past a custom threshold (e.g., over 150% of the average), instantly drawing your attention to critical moments.
Full Color Customization: Change every color to match your chart's theme, including separate colors for bullish/bearish moves, the background, and the border.
How to Use It
The VSA Volume HUD is a powerful confirmation tool. Use it to:
Confirm Breakouts: Look for a spike in Volume vs. Average and RVOL as price breaks a key level.
Spot Exhaustion: Notice high volume on a narrow-range candle after a long trend, visible through the Range/ATR metric.
Gauge Conviction: Use the Advanced Coloring to see if volume is supporting the price move (e.g., green volume on a green candle) or diverging from it.
Kelly Position Size CalculatorThis position sizing calculator implements the Kelly Criterion, developed by John L. Kelly Jr. at Bell Laboratories in 1956, to determine mathematically optimal position sizes for maximizing long-term wealth growth. Unlike arbitrary position sizing methods, this tool provides a scientifically solution based on your strategy's actual performance statistics and incorporates modern refinements from over six decades of academic research.
The Kelly Criterion addresses a fundamental question in capital allocation: "What fraction of capital should be allocated to each opportunity to maximize growth while avoiding ruin?" This question has profound implications for financial markets, where traders and investors constantly face decisions about optimal capital allocation (Van Tharp, 2007).
Theoretical Foundation
The Kelly Criterion for binary outcomes is expressed as f* = (bp - q) / b, where f* represents the optimal fraction of capital to allocate, b denotes the risk-reward ratio, p indicates the probability of success, and q represents the probability of loss (Kelly, 1956). This formula maximizes the expected logarithm of wealth, ensuring maximum long-term growth rate while avoiding the risk of ruin.
The mathematical elegance of Kelly's approach lies in its derivation from information theory. Kelly's original work was motivated by Claude Shannon's information theory (Shannon, 1948), recognizing that maximizing the logarithm of wealth is equivalent to maximizing the rate of information transmission. This connection between information theory and wealth accumulation provides a deep theoretical foundation for optimal position sizing.
The logarithmic utility function underlying the Kelly Criterion naturally embodies several desirable properties for capital management. It exhibits decreasing marginal utility, penalizes large losses more severely than it rewards equivalent gains, and focuses on geometric rather than arithmetic mean returns, which is appropriate for compounding scenarios (Thorp, 2006).
Scientific Implementation
This calculator extends beyond basic Kelly implementation by incorporating state of the art refinements from academic research:
Parameter Uncertainty Adjustment: Following Michaud (1989), the implementation applies Bayesian shrinkage to account for parameter estimation error inherent in small sample sizes. The adjustment formula f_adjusted = f_kelly × confidence_factor + f_conservative × (1 - confidence_factor) addresses the overconfidence bias documented by Baker and McHale (2012), where the confidence factor increases with sample size and the conservative estimate equals 0.25 (quarter Kelly).
Sample Size Confidence: The reliability of Kelly calculations depends critically on sample size. Research by Browne and Whitt (1996) provides theoretical guidance on minimum sample requirements, suggesting that at least 30 independent observations are necessary for meaningful parameter estimates, with 100 or more trades providing reliable estimates for most trading strategies.
Universal Asset Compatibility: The calculator employs intelligent asset detection using TradingView's built-in symbol information, automatically adapting calculations for different asset classes without manual configuration.
ASSET SPECIFIC IMPLEMENTATION
Equity Markets: For stocks and ETFs, position sizing follows the calculation Shares = floor(Kelly Fraction × Account Size / Share Price). This straightforward approach reflects whole share constraints while accommodating fractional share trading capabilities.
Foreign Exchange Markets: Forex markets require lot-based calculations following Lot Size = Kelly Fraction × Account Size / (100,000 × Base Currency Value). The calculator automatically handles major currency pairs with appropriate pip value calculations, following industry standards described by Archer (2010).
Futures Markets: Futures position sizing accounts for leverage and margin requirements through Contracts = floor(Kelly Fraction × Account Size / Margin Requirement). The calculator estimates margin requirements as a percentage of contract notional value, with specific adjustments for micro-futures contracts that have smaller sizes and reduced margin requirements (Kaufman, 2013).
Index and Commodity Markets: These markets combine characteristics of both equity and futures markets. The calculator automatically detects whether instruments are cash-settled or futures-based, applying appropriate sizing methodologies with correct point value calculations.
Risk Management Integration
The calculator integrates sophisticated risk assessment through two primary modes:
Stop Loss Integration: When fixed stop-loss levels are defined, risk calculation follows Risk per Trade = Position Size × Stop Loss Distance. This ensures that the Kelly fraction accounts for actual risk exposure rather than theoretical maximum loss, with stop-loss distance measured in appropriate units for each asset class.
Strategy Drawdown Assessment: For discretionary exit strategies, risk estimation uses maximum historical drawdown through Risk per Trade = Position Value × (Maximum Drawdown / 100). This approach assumes that individual trade losses will not exceed the strategy's historical maximum drawdown, providing a reasonable estimate for strategies with well-defined risk characteristics.
Fractional Kelly Approaches
Pure Kelly sizing can produce substantial volatility, leading many practitioners to adopt fractional Kelly approaches. MacLean, Sanegre, Zhao, and Ziemba (2004) analyze the trade-offs between growth rate and volatility, demonstrating that half-Kelly typically reduces volatility by approximately 75% while sacrificing only 25% of the growth rate.
The calculator provides three primary Kelly modes to accommodate different risk preferences and experience levels. Full Kelly maximizes growth rate while accepting higher volatility, making it suitable for experienced practitioners with strong risk tolerance and robust capital bases. Half Kelly offers a balanced approach popular among professional traders, providing optimal risk-return balance by reducing volatility significantly while maintaining substantial growth potential. Quarter Kelly implements a conservative approach with low volatility, recommended for risk-averse traders or those new to Kelly methodology who prefer gradual introduction to optimal position sizing principles.
Empirical Validation and Performance
Extensive academic research supports the theoretical advantages of Kelly sizing. Hakansson and Ziemba (1995) provide a comprehensive review of Kelly applications in finance, documenting superior long-term performance across various market conditions and asset classes. Estrada (2008) analyzes Kelly performance in international equity markets, finding that Kelly-based strategies consistently outperform fixed position sizing approaches over extended periods across 19 developed markets over a 30-year period.
Several prominent investment firms have successfully implemented Kelly-based position sizing. Pabrai (2007) documents the application of Kelly principles at Berkshire Hathaway, noting Warren Buffett's concentrated portfolio approach aligns closely with Kelly optimal sizing for high-conviction investments. Quantitative hedge funds, including Renaissance Technologies and AQR, have incorporated Kelly-based risk management into their systematic trading strategies.
Practical Implementation Guidelines
Successful Kelly implementation requires systematic application with attention to several critical factors:
Parameter Estimation: Accurate parameter estimation represents the greatest challenge in practical Kelly implementation. Brown (1976) notes that small errors in probability estimates can lead to significant deviations from optimal performance. The calculator addresses this through Bayesian adjustments and confidence measures.
Sample Size Requirements: Users should begin with conservative fractional Kelly approaches until achieving sufficient historical data. Strategies with fewer than 30 trades may produce unreliable Kelly estimates, regardless of adjustments. Full confidence typically requires 100 or more independent trade observations.
Market Regime Considerations: Parameters that accurately describe historical performance may not reflect future market conditions. Ziemba (2003) recommends regular parameter updates and conservative adjustments when market conditions change significantly.
Professional Features and Customization
The calculator provides comprehensive customization options for professional applications:
Multiple Color Schemes: Eight professional color themes (Gold, EdgeTools, Behavioral, Quant, Ocean, Fire, Matrix, Arctic) with dark and light theme compatibility ensure optimal visibility across different trading environments.
Flexible Display Options: Adjustable table size and position accommodate various chart layouts and user preferences, while maintaining analytical depth and clarity.
Comprehensive Results: The results table presents essential information including asset specifications, strategy statistics, Kelly calculations, sample confidence measures, position values, risk assessments, and final position sizes in appropriate units for each asset class.
Limitations and Considerations
Like any analytical tool, the Kelly Criterion has important limitations that users must understand:
Stationarity Assumption: The Kelly Criterion assumes that historical strategy statistics represent future performance characteristics. Non-stationary market conditions may invalidate this assumption, as noted by Lo and MacKinlay (1999).
Independence Requirement: Each trade should be independent to avoid correlation effects. Many trading strategies exhibit serial correlation in returns, which can affect optimal position sizing and may require adjustments for portfolio applications.
Parameter Sensitivity: Kelly calculations are sensitive to parameter accuracy. Regular calibration and conservative approaches are essential when parameter uncertainty is high.
Transaction Costs: The implementation incorporates user-defined transaction costs but assumes these remain constant across different position sizes and market conditions, following Ziemba (2003).
Advanced Applications and Extensions
Multi-Asset Portfolio Considerations: While this calculator optimizes individual position sizes, portfolio-level applications require additional considerations for correlation effects and aggregate risk management. Simplified portfolio approaches include treating positions independently with correlation adjustments.
Behavioral Factors: Behavioral finance research reveals systematic biases that can interfere with Kelly implementation. Kahneman and Tversky (1979) document loss aversion, overconfidence, and other cognitive biases that lead traders to deviate from optimal strategies. Successful implementation requires disciplined adherence to calculated recommendations.
Time-Varying Parameters: Advanced implementations may incorporate time-varying parameter models that adjust Kelly recommendations based on changing market conditions, though these require sophisticated econometric techniques and substantial computational resources.
Comprehensive Usage Instructions and Practical Examples
Implementation begins with loading the calculator on your desired trading instrument's chart. The system automatically detects asset type across stocks, forex, futures, and cryptocurrency markets while extracting current price information. Navigation to the indicator settings allows input of your specific strategy parameters.
Strategy statistics configuration requires careful attention to several key metrics. The win rate should be calculated from your backtest results using the formula of winning trades divided by total trades multiplied by 100. Average win represents the sum of all profitable trades divided by the number of winning trades, while average loss calculates the sum of all losing trades divided by the number of losing trades, entered as a positive number. The total historical trades parameter requires the complete number of trades in your backtest, with a minimum of 30 trades recommended for basic functionality and 100 or more trades optimal for statistical reliability. Account size should reflect your available trading capital, specifically the risk capital allocated for trading rather than total net worth.
Risk management configuration adapts to your specific trading approach. The stop loss setting should be enabled if you employ fixed stop-loss exits, with the stop loss distance specified in appropriate units depending on the asset class. For stocks, this distance is measured in dollars, for forex in pips, and for futures in ticks. When stop losses are not used, the maximum strategy drawdown percentage from your backtest provides the risk assessment baseline. Kelly mode selection offers three primary approaches: Full Kelly for aggressive growth with higher volatility suitable for experienced practitioners, Half Kelly for balanced risk-return optimization popular among professional traders, and Quarter Kelly for conservative approaches with reduced volatility.
Display customization ensures optimal integration with your trading environment. Eight professional color themes provide optimization for different chart backgrounds and personal preferences. Table position selection allows optimal placement within your chart layout, while table size adjustment ensures readability across different screen resolutions and viewing preferences.
Detailed Practical Examples
Example 1: SPY Swing Trading Strategy
Consider a professionally developed swing trading strategy for SPY (S&P 500 ETF) with backtesting results spanning 166 total trades. The strategy achieved 110 winning trades, representing a 66.3% win rate, with an average winning trade of $2,200 and average losing trade of $862. The maximum drawdown reached 31.4% during the testing period, and the available trading capital amounts to $25,000. This strategy employs discretionary exits without fixed stop losses.
Implementation requires loading the calculator on the SPY daily chart and configuring the parameters accordingly. The win rate input receives 66.3, while average win and loss inputs receive 2200 and 862 respectively. Total historical trades input requires 166, with account size set to 25000. The stop loss function remains disabled due to the discretionary exit approach, with maximum strategy drawdown set to 31.4%. Half Kelly mode provides the optimal balance between growth and risk management for this application.
The calculator generates several key outputs for this scenario. The risk-reward ratio calculates automatically to 2.55, while the Kelly fraction reaches approximately 53% before scientific adjustments. Sample confidence achieves 100% given the 166 trades providing high statistical confidence. The recommended position settles at approximately 27% after Half Kelly and Bayesian adjustment factors. Position value reaches approximately $6,750, translating to 16 shares at a $420 SPY price. Risk per trade amounts to approximately $2,110, representing 31.4% of position value, with expected value per trade reaching approximately $1,466. This recommendation represents the mathematically optimal balance between growth potential and risk management for this specific strategy profile.
Example 2: EURUSD Day Trading with Stop Losses
A high-frequency EURUSD day trading strategy demonstrates different parameter requirements compared to swing trading approaches. This strategy encompasses 89 total trades with a 58% win rate, generating an average winning trade of $180 and average losing trade of $95. The maximum drawdown reached 12% during testing, with available capital of $10,000. The strategy employs fixed stop losses at 25 pips and take profit targets at 45 pips, providing clear risk-reward parameters.
Implementation begins with loading the calculator on the EURUSD 1-hour chart for appropriate timeframe alignment. Parameter configuration includes win rate at 58, average win at 180, and average loss at 95. Total historical trades input receives 89, with account size set to 10000. The stop loss function is enabled with distance set to 25 pips, reflecting the fixed exit strategy. Quarter Kelly mode provides conservative positioning due to the smaller sample size compared to the previous example.
Results demonstrate the impact of smaller sample sizes on Kelly calculations. The risk-reward ratio calculates to 1.89, while the Kelly fraction reaches approximately 32% before adjustments. Sample confidence achieves 89%, providing moderate statistical confidence given the 89 trades. The recommended position settles at approximately 7% after Quarter Kelly application and Bayesian shrinkage adjustment for the smaller sample. Position value amounts to approximately $700, translating to 0.07 standard lots. Risk per trade reaches approximately $175, calculated as 25 pips multiplied by lot size and pip value, with expected value per trade at approximately $49. This conservative position sizing reflects the smaller sample size, with position sizes expected to increase as trade count surpasses 100 and statistical confidence improves.
Example 3: ES1! Futures Systematic Strategy
Systematic futures trading presents unique considerations for Kelly criterion application, as demonstrated by an E-mini S&P 500 futures strategy encompassing 234 total trades. This systematic approach achieved a 45% win rate with an average winning trade of $1,850 and average losing trade of $720. The maximum drawdown reached 18% during the testing period, with available capital of $50,000. The strategy employs 15-tick stop losses with contract specifications of $50 per tick, providing precise risk control mechanisms.
Implementation involves loading the calculator on the ES1! 15-minute chart to align with the systematic trading timeframe. Parameter configuration includes win rate at 45, average win at 1850, and average loss at 720. Total historical trades receives 234, providing robust statistical foundation, with account size set to 50000. The stop loss function is enabled with distance set to 15 ticks, reflecting the systematic exit methodology. Half Kelly mode balances growth potential with appropriate risk management for futures trading.
Results illustrate how favorable risk-reward ratios can support meaningful position sizing despite lower win rates. The risk-reward ratio calculates to 2.57, while the Kelly fraction reaches approximately 16%, lower than previous examples due to the sub-50% win rate. Sample confidence achieves 100% given the 234 trades providing high statistical confidence. The recommended position settles at approximately 8% after Half Kelly adjustment. Estimated margin per contract amounts to approximately $2,500, resulting in a single contract allocation. Position value reaches approximately $2,500, with risk per trade at $750, calculated as 15 ticks multiplied by $50 per tick. Expected value per trade amounts to approximately $508. Despite the lower win rate, the favorable risk-reward ratio supports meaningful position sizing, with single contract allocation reflecting appropriate leverage management for futures trading.
Example 4: MES1! Micro-Futures for Smaller Accounts
Micro-futures contracts provide enhanced accessibility for smaller trading accounts while maintaining identical strategy characteristics. Using the same systematic strategy statistics from the previous example but with available capital of $15,000 and micro-futures specifications of $5 per tick with reduced margin requirements, the implementation demonstrates improved position sizing granularity.
Kelly calculations remain identical to the full-sized contract example, maintaining the same risk-reward dynamics and statistical foundations. However, estimated margin per contract reduces to approximately $250 for micro-contracts, enabling allocation of 4-5 micro-contracts. Position value reaches approximately $1,200, while risk per trade calculates to $75, derived from 15 ticks multiplied by $5 per tick. This granularity advantage provides better position size precision for smaller accounts, enabling more accurate Kelly implementation without requiring large capital commitments.
Example 5: Bitcoin Swing Trading
Cryptocurrency markets present unique challenges requiring modified Kelly application approaches. A Bitcoin swing trading strategy on BTCUSD encompasses 67 total trades with a 71% win rate, generating average winning trades of $3,200 and average losing trades of $1,400. Maximum drawdown reached 28% during testing, with available capital of $30,000. The strategy employs technical analysis for exits without fixed stop losses, relying on price action and momentum indicators.
Implementation requires conservative approaches due to cryptocurrency volatility characteristics. Quarter Kelly mode is recommended despite the high win rate to account for crypto market unpredictability. Expected position sizing remains reduced due to the limited sample size of 67 trades, requiring additional caution until statistical confidence improves. Regular parameter updates are strongly recommended due to cryptocurrency market evolution and changing volatility patterns that can significantly impact strategy performance characteristics.
Advanced Usage Scenarios
Portfolio position sizing requires sophisticated consideration when running multiple strategies simultaneously. Each strategy should have its Kelly fraction calculated independently to maintain mathematical integrity. However, correlation adjustments become necessary when strategies exhibit related performance patterns. Moderately correlated strategies should receive individual position size reductions of 10-20% to account for overlapping risk exposure. Aggregate portfolio risk monitoring ensures total exposure remains within acceptable limits across all active strategies. Professional practitioners often consider using lower fractional Kelly approaches, such as Quarter Kelly, when running multiple strategies simultaneously to provide additional safety margins.
Parameter sensitivity analysis forms a critical component of professional Kelly implementation. Regular validation procedures should include monthly parameter updates using rolling 100-trade windows to capture evolving market conditions while maintaining statistical relevance. Sensitivity testing involves varying win rates by ±5% and average win/loss ratios by ±10% to assess recommendation stability under different parameter assumptions. Out-of-sample validation reserves 20% of historical data for parameter verification, ensuring that optimization doesn't create curve-fitted results. Regime change detection monitors actual performance against expected metrics, triggering parameter reassessment when significant deviations occur.
Risk management integration requires professional overlay considerations beyond pure Kelly calculations. Daily loss limits should cease trading when daily losses exceed twice the calculated risk per trade, preventing emotional decision-making during adverse periods. Maximum position limits should never exceed 25% of account value in any single position regardless of Kelly recommendations, maintaining diversification principles. Correlation monitoring reduces position sizes when holding multiple correlated positions that move together during market stress. Volatility adjustments consider reducing position sizes during periods of elevated VIX above 25 for equity strategies, adapting to changing market conditions.
Troubleshooting and Optimization
Professional implementation often encounters specific challenges requiring systematic troubleshooting approaches. Zero position size displays typically result from insufficient capital for minimum position sizes, negative expected values, or extremely conservative Kelly calculations. Solutions include increasing account size, verifying strategy statistics for accuracy, considering Quarter Kelly mode for conservative approaches, or reassessing overall strategy viability when fundamental issues exist.
Extremely high Kelly fractions exceeding 50% usually indicate underlying problems with parameter estimation. Common causes include unrealistic win rates, inflated risk-reward ratios, or curve-fitted backtest results that don't reflect genuine trading conditions. Solutions require verifying backtest methodology, including all transaction costs in calculations, testing strategies on out-of-sample data, and using conservative fractional Kelly approaches until parameter reliability improves.
Low sample confidence below 50% reflects insufficient historical trades for reliable parameter estimation. This situation demands gathering additional trading data, using Quarter Kelly approaches until reaching 100 or more trades, applying extra conservatism in position sizing, and considering paper trading to build statistical foundations without capital risk.
Inconsistent results across similar strategies often stem from parameter estimation differences, market regime changes, or strategy degradation over time. Professional solutions include standardizing backtest methodology across all strategies, updating parameters regularly to reflect current conditions, and monitoring live performance against expectations to identify deteriorating strategies.
Position sizes that appear inappropriately large or small require careful validation against traditional risk management principles. Professional standards recommend never risking more than 2-3% per trade regardless of Kelly calculations. Calibration should begin with Quarter Kelly approaches, gradually increasing as comfort and confidence develop. Most institutional traders utilize 25-50% of full Kelly recommendations to balance growth with prudent risk management.
Market condition adjustments require dynamic approaches to Kelly implementation. Trending markets may support full Kelly recommendations when directional momentum provides favorable conditions. Ranging or volatile markets typically warrant reducing to Half or Quarter Kelly to account for increased uncertainty. High correlation periods demand reducing individual position sizes when multiple positions move together, concentrating risk exposure. News and event periods often justify temporary position size reductions during high-impact releases that can create unpredictable market movements.
Performance monitoring requires systematic protocols to ensure Kelly implementation remains effective over time. Weekly reviews should compare actual versus expected win rates and average win/loss ratios to identify parameter drift or strategy degradation. Position size efficiency and execution quality monitoring ensures that calculated recommendations translate effectively into actual trading results. Tracking correlation between calculated and realized risk helps identify discrepancies between theoretical and practical risk exposure.
Monthly calibration provides more comprehensive parameter assessment using the most recent 100 trades to maintain statistical relevance while capturing current market conditions. Kelly mode appropriateness requires reassessment based on recent market volatility and performance characteristics, potentially shifting between Full, Half, and Quarter Kelly approaches as conditions change. Transaction cost evaluation ensures that commission structures, spreads, and slippage estimates remain accurate and current.
Quarterly strategic reviews encompass comprehensive strategy performance analysis comparing long-term results against expectations and identifying trends in effectiveness. Market regime assessment evaluates parameter stability across different market conditions, determining whether strategy characteristics remain consistent or require fundamental adjustments. Strategic modifications to position sizing methodology may become necessary as markets evolve or trading approaches mature, ensuring that Kelly implementation continues supporting optimal capital allocation objectives.
Professional Applications
This calculator serves diverse professional applications across the financial industry. Quantitative hedge funds utilize the implementation for systematic position sizing within algorithmic trading frameworks, where mathematical precision and consistent application prove essential for institutional capital management. Professional discretionary traders benefit from optimized position management that removes emotional bias while maintaining flexibility for market-specific adjustments. Portfolio managers employ the calculator for developing risk-adjusted allocation strategies that enhance returns while maintaining prudent risk controls across diverse asset classes and investment strategies.
Individual traders seeking mathematical optimization of capital allocation find the calculator provides institutional-grade methodology previously available only to professional money managers. The Kelly Criterion establishes theoretical foundation for optimal capital allocation across both single strategies and multiple trading systems, offering significant advantages over arbitrary position sizing methods that rely on intuition or fixed percentage approaches. Professional implementation ensures consistent application of mathematically sound principles while adapting to changing market conditions and strategy performance characteristics.
Conclusion
The Kelly Criterion represents one of the few mathematically optimal solutions to fundamental investment problems. When properly understood and carefully implemented, it provides significant competitive advantage in financial markets. This calculator implements modern refinements to Kelly's original formula while maintaining accessibility for practical trading applications.
Success with Kelly requires ongoing learning, systematic application, and continuous refinement based on market feedback and evolving research. Users who master Kelly principles and implement them systematically can expect superior risk-adjusted returns and more consistent capital growth over extended periods.
The extensive academic literature provides rich resources for deeper study, while practical experience builds the intuition necessary for effective implementation. Regular parameter updates, conservative approaches with limited data, and disciplined adherence to calculated recommendations are essential for optimal results.
References
Archer, M. D. (2010). Getting Started in Currency Trading: Winning in Today's Forex Market (3rd ed.). John Wiley & Sons.
Baker, R. D., & McHale, I. G. (2012). An empirical Bayes approach to optimising betting strategies. Journal of the Royal Statistical Society: Series D (The Statistician), 61(1), 75-92.
Breiman, L. (1961). Optimal gambling systems for favorable games. In J. Neyman (Ed.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (pp. 65-78). University of California Press.
Brown, D. B. (1976). Optimal portfolio growth: Logarithmic utility and the Kelly criterion. In W. T. Ziemba & R. G. Vickson (Eds.), Stochastic Optimization Models in Finance (pp. 1-23). Academic Press.
Browne, S., & Whitt, W. (1996). Portfolio choice and the Bayesian Kelly criterion. Advances in Applied Probability, 28(4), 1145-1176.
Estrada, J. (2008). Geometric mean maximization: An overlooked portfolio approach? The Journal of Investing, 17(4), 134-147.
Hakansson, N. H., & Ziemba, W. T. (1995). Capital growth theory. In R. A. Jarrow, V. Maksimovic, & W. T. Ziemba (Eds.), Handbooks in Operations Research and Management Science (Vol. 9, pp. 65-86). Elsevier.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291.
Kaufman, P. J. (2013). Trading Systems and Methods (5th ed.). John Wiley & Sons.
Kelly Jr, J. L. (1956). A new interpretation of information rate. Bell System Technical Journal, 35(4), 917-926.
Lo, A. W., & MacKinlay, A. C. (1999). A Non-Random Walk Down Wall Street. Princeton University Press.
MacLean, L. C., Sanegre, E. O., Zhao, Y., & Ziemba, W. T. (2004). Capital growth with security. Journal of Economic Dynamics and Control, 28(4), 937-954.
MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (2011). The Kelly Capital Growth Investment Criterion: Theory and Practice. World Scientific.
Michaud, R. O. (1989). The Markowitz optimization enigma: Is 'optimized' optimal? Financial Analysts Journal, 45(1), 31-42.
Pabrai, M. (2007). The Dhandho Investor: The Low-Risk Value Method to High Returns. John Wiley & Sons.
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.
Tharp, V. K. (2007). Trade Your Way to Financial Freedom (2nd ed.). McGraw-Hill.
Thorp, E. O. (2006). The Kelly criterion in blackjack sports betting, and the stock market. In L. C. MacLean, E. O. Thorp, & W. T. Ziemba (Eds.), The Kelly Capital Growth Investment Criterion: Theory and Practice (pp. 789-832). World Scientific.
Van Tharp, K. (2007). Trade Your Way to Financial Freedom (2nd ed.). McGraw-Hill Education.
Vince, R. (1992). The Mathematics of Money Management: Risk Analysis Techniques for Traders. John Wiley & Sons.
Vince, R., & Zhu, H. (2015). Optimal betting under parameter uncertainty. Journal of Statistical Planning and Inference, 161, 19-31.
Ziemba, W. T. (2003). The Stochastic Programming Approach to Asset, Liability, and Wealth Management. The Research Foundation of AIMR.
Further Reading
For comprehensive understanding of Kelly Criterion applications and advanced implementations:
MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (2011). The Kelly Capital Growth Investment Criterion: Theory and Practice. World Scientific.
Vince, R. (1992). The Mathematics of Money Management: Risk Analysis Techniques for Traders. John Wiley & Sons.
Thorp, E. O. (2017). A Man for All Markets: From Las Vegas to Wall Street. Random House.
Cover, T. M., & Thomas, J. A. (2006). Elements of Information Theory (2nd ed.). John Wiley & Sons.
Ziemba, W. T., & Vickson, R. G. (Eds.). (2006). Stochastic Optimization Models in Finance. World Scientific.
Daily Manipulation Probability Dashboard📜 Summary
Tired of getting stopped out on a "Judas Swing" just before the price moves in your intended direction? This indicator is designed to give you a statistical edge by quantifying the daily manipulation move.
The Daily Manipulation Probability Dashboard analyzes thousands of historical trading days to reveal the probability of the initial "stop-hunt" or "fakeout" move reaching certain percentage levels. It presents this data in a clean, intuitive dashboard right on your chart, helping you make more data-driven decisions about stop-loss placement and entry timing.
🧠 The Core Concept
The logic is simple but powerful. For every trading day, we measure two things:
Amplitude Above Open (AAO): The distance price travels up from the daily open (High - Open).
Amplitude Below Open (ABO): The distance price travels down from the daily open (Open - Low).
The indicator defines the "Manipulation" as the smaller of these two moves. The idea is that this smaller move often acts as a liquidity grab to trap traders before the day's primary, larger move ("Distribution") begins.
This tool focuses exclusively on providing deep statistical insight into this crucial manipulation phase.
🛠️ How to Use This Tool
This dashboard is designed to be a practical part of your daily analysis and trade planning.
1. Smarter Stop-Loss Placement
This is the primary use case. The "Prob. (%)" column tells you the historical chance of the manipulation move being at least a certain size.
Example: If the table shows that for EURUSD, the ≥ 0.25% level has a probability of 30%, you can flip this information: there is a 70% probability that the daily manipulation move will be less than 0.25%.
Action: Placing your stop-loss just beyond a level with a low probability gives you a statistically sound buffer against typical stop-hunts.
2. Entry Timing and Patience
The live arrow (→) shows you where the current day's manipulation falls.
Example: If the arrow is pointing at ≥ 0.10% and you know there is a high probability (e.g., 60%) of the manipulation reaching ≥ 0.20%, you might wait for a deeper pullback before entering, anticipating that the "Judas Swing" hasn't completed yet.
3. Assessing Daily Character
Quickly see if the current day's action is unusual. If the manipulation move is already in a very low probability zone (e.g., > 1.00%), it might indicate that your Bias is wrong, or signal a high-volatility day or a potential trend reversal.
📊 Understanding the Dashboard
Ticker: The top-right shows the current symbol you are analyzing.
→ (Arrow): Points to the row that corresponds to the current, live day's manipulation amplitude.
Manip. Level: The percentage threshold being analyzed (e.g., ≥ 0.20%).
Days Analyzed: The raw count of historical days where the manipulation move met or exceeded this level.
Prob. (%): The key statistic. The cumulative probability of the manipulation move being at least the size of the level.
⚙️ Settings
Position: Choose where you want the dashboard to appear on your chart.
Text Size: Adjust the font size for readability.
Max Historical Days to Analyze: Set the number of past daily candles to include in the statistical analysis. A larger number provides a more robust sample size.
I believe this tool provides a unique, data-driven edge for intraday traders across all markets (Forex, Crypto, Stocks, Indices). Your feedback and suggestions are highly welcome!
- @traderprimez
Uptrick: Universal Z-Score ValuationOverview
The Uptrick: Universal Z-Score Valuation is a tool designed to help traders spot when the market might be overreacting—whether that’s on the upside or the downside. It does this by combining the Z-scores of multiple key indicators into a single average, letting you see how far the current market conditions have stretched away from “normal.” This average is shown as a smooth line, supported by color-coded visuals, signal markers, optional background highlights, and a live breakdown table that shows the contribution of each indicator in real time. The focus here is on spotting potential reversals, not following trends. The indicator works well across all timeframes and asset classes, from fast intraday charts like the 1-minute and 5-minute, to higher timeframes such as the 4-hour, daily, or even weekly. Its universal design makes it suitable for any market — whether you're trading crypto, stocks, forex, or commodities.
Introduction
To understand what this indicator does, let’s start with the idea of a Z-score. In simple terms, a Z-score tells you how far a number is from the average of its recent history, measured in standard deviations. If the price of an asset is two standard deviations above its mean, that means it’s statistically “rare” or extended. That doesn’t guarantee a reversal—but it suggests the move is unusual enough to pay attention.
This concept isn’t new, but what this indicator does differently is apply the Z-score to a wide set of market signals—not just price. It looks at momentum, volatility, volume, risk-adjusted performance, and even institutional price baselines. Each of those indicators is normalized using Z-scores, and then they’re combined into one average. This gives you a single, easy-to-read line that summarizes whether the entire market is behaving abnormally. Instead of reacting to one indicator, you’re reacting to a statistically balanced blend.
Purpose
The goal of this script is to catch turning points—places where the market may be topping out or bottoming after becoming overstretched. It’s built for traders who want to fade sharp moves rather than follow trends. Think of moments when price explodes upward and starts pulling away from every moving average, volume spikes, volatility rises, and RSI shoots up. This tool is meant to spot those situations—not just when price is stretched, but when multiple different indicators agree that something is overdone.
Originality and Uniqueness
Most indicators that use Z-scores only apply them to one thing—price, RSI, or maybe Bollinger Bands. This one is different because it treats each indicator as a contributor to the full picture. You decide which ones to include, and the script averages them out. This makes the tool flexible but also deeply informative.
It doesn’t rely on complex or hidden math. It uses basic Z-score formulas, applies them to well-known indicators, and shows you the result. What makes it unique is the way it brings those signals together—statistically, visually, and interactively—so you can see what’s happening in the moment with full transparency. It’s not trying to be flashy or predictive. It’s just showing you when things have gone too far, too fast.
Inputs and Parameters
This indicator includes a wide range of configurable inputs, allowing users to customize which components are included in the Z-score average, how each indicator is calculated, and how results are displayed visually. Below is a detailed explanation of each input:
General Settings
Z-Score Lookback (default: 100): Number of bars used to calculate the mean and standard deviation for Z-score normalization. Larger values smooth the Z-scores; smaller values make them more reactive.
Bar Color Mode (default: None): Determines how bars are visually colored. Options include: None: No candle coloring applied. - Heat: Smooth gradient based on the Z-score value. - Latest Signal: Applies a solid color based on the most recent buy or sell signal
Boolean - General
Plot Universal Valuation Line (default: true): If enabled, plots the average Z-score (zAvg) line in the separate pane.
Show Signals (default: true): Displays labels ("𝓤𝓹" for buy, "𝓓𝓸𝔀𝓷" for sell) when zAvg crosses above or below user-defined thresholds.
Show Z-Score Table (default: true): Displays a live table listing each enabled indicator's Z-score and the current average.
Select Indicators
These toggles enable or disable each indicator from contributing to the Z-score average:
Use VWAP Z-Score (default: true)
Use Sortino Z-Score (default: true)
Use ROC Z-Score (default: true)
Use Price Z-Score (default: true)
Use MACD Histogram Z-Score (default: false)
Use Bollinger %B Z-Score (default: false)
Use Stochastic K Z-Score (default: false)
Use Volume Z-Score (default: false)
Use ATR Z-Score (default: false)
Use RSI Z-Score (default: false)
Use Omega Z-Score (default: true)
Use Sharpe Z-Score (default: true)
Only enabled indicators are included in the average. This modular design allows traders to tailor the signal mix to their preferences.
Indicator Lengths
These inputs control how each individual indicator is calculated:
MACD Fast Length (default: 12)
MACD Slow Length (default: 26)
MACD Signal Length (default: 9)
Bollinger Basis Length (default: 20): Used to compute the Bollinger %B.
Bollinger Deviation Multiplier (default: 2.0): Standard deviation multiplier for the Bollinger Band calculation.
Stochastic Length (default: 14)
ATR Length (default: 14)
RSI Length (default: 14)
ROC Length (default: 10)
Zones
These thresholds define key signal levels for the Z-score average:
Neutral Line Level (default: 0): Baseline for the average Z-score.
Bullish Zone Level (default: -1): Optional intermediate zone suggesting early bullish conditions.
Bearish Zone Level (default: 1): Optional intermediate zone suggesting early bearish conditions.
Z = +2 Line Level (default: 2): Primary threshold for bearish signals.
Z = +3 Line Level (default: 3): Extreme bearish warning level.
Z = -2 Line Level (default: -2): Primary threshold for bullish signals.
Z = -3 Line Level (default: -3): Extreme bullish warning level.
These zone levels are used to generate signals, fill background shading, and draw horizontal lines for visual reference.
Why These Indicators Were Merged
Each indicator in this script was chosen for a specific reason. They all measure something different but complementary.
The VWAP Z-score helps you see when price has moved far from the volume-weighted average, often used by institutions.
Sortino Ratio Z-score focuses only on downside risk, which is often more relevant to traders than overall volatility.
ROC Z-score shows how fast price is changing—strong momentum may burn out quickly.
Price Z-score is the raw measure of how far current price has moved from its mean.
RSI Z-score shows whether momentum itself is stretched.
MACD Histogram Z-score captures shifts in trend strength and acceleration.
%B (Bollinger) Z-score indicates how close price is to the upper or lower volatility envelope.
Stochastic K Z-score gives a sense of how high or low price is relative to its recent range.
Volume Z-score shows when trading activity is unusually high or low.
ATR Z-score gives a read on volatility, showing if price movement is expanding or contracting.
Sharpe Z-score measures reward-to-risk performance, useful for evaluating trend quality.
Omega Z-score looks at the ratio of good returns to bad ones, offering a more nuanced view of efficiency.
By normalizing each of these using Z-scores and averaging only the ones you turn on, the script creates a flexible, balanced view of the market’s statistical stretch.
Calculations
The core formula is the standard Z-score:
Z = (current value - average) / standard deviation
Every indicator uses this formula after it’s calculated using your chosen settings. For example, RSI is first calculated as usual, then its Z-score is calculated over your selected lookback period. The script does this for every indicator you enable. Then it averages those Z-scores together to create a single value: zAvg. That value is plotted and used to generate visual cues, signals, table values, background color changes, and candle coloring.
Sequence
Each selected indicator is calculated using your custom input lengths.
The Z-score of each indicator is computed using the shared lookback period.
All active Z-scores are added up and averaged.
The resulting zAvg value is plotted as a line.
Signal conditions check if zAvg crosses user-defined thresholds (default: ±2).
If enabled, the script plots buy/sell signal labels at those crossover points.
The candle color is updated using your selected mode (heatmap or signal-based).
If extreme Z-scores are reached, background highlighting is applied.
A live table updates with each individual Z-score so you know what’s driving the signal.
Features
This script isn’t just about stats—it’s about making them usable in real time. Every feature has a clear reason to exist, and they’re all there to give you a better read on market conditions.
1. Universal Z-Score Line
This is your primary reference. It reflects the average Z-score across all selected indicators. The line updates live and is color-coded to show how far it is from neutral. The further it gets from 0, the brighter the color becomes—cyan for deeply oversold conditions, magenta for overbought. This gives you instant feedback on how statistically “hot” or “cold” the market is, without needing to read any numbers.
2. Signal Labels (“𝓤𝓹” and “𝓓𝓸𝔀𝓷”)
When the average Z-score drops below your lower bound, you’ll see a "𝓤𝓹" label below the bar, suggesting potential bullish reversal conditions. When it rises above the upper bound, a "𝓓𝓸𝔀𝓷" label is shown above the bar—indicating possible bearish exhaustion. These labels are visually clear and minimal so they don’t clutter your chart. They're based on clear crossover logic and do not repaint.
3. Real-Time Z-Score Table
The table shows each indicator's individual Z-score and the final average. It updates every bar, giving you a transparent breakdown of what’s happening under the hood. If the market is showing an extreme average score, this table helps you pinpoint which indicators are contributing the most—so you’re not just guessing where the pressure is coming from.
4. Bar Coloring Modes
You can choose from three modes:
None: Keeps your candles clean and untouched.
Heat: Applies a smooth gradient color based on Z-score intensity. As conditions become more extreme, candle color transitions from neutral to either cyan (bullish pressure) or magenta (bearish pressure).
Latest Signal: Applies hard coloring based on the most recent signal—greenish for a buy, purple for a sell. This mode is great for tracking market state at a glance without relying on a gradient.
Every part of the candle is colored—body, wick, and border—for full visibility.
5. Background Highlighting
When zAvg enters an extreme zone (typically above +2 or below -2), the background shifts color to reflect the market’s intensity. These changes aren’t overwhelming—they’re light fills that act as ambient warnings, helping you stay aware of when price might be reaching a tipping point.
6. Customizable Zone Lines and Fills
You can define what counts as neutral, overbought, and oversold using manual inputs. Horizontal lines show your thresholds, and shaded regions highlight the most extreme zones (+2 to +3 and -2 to -3). These lines give you visual structure to understand where price currently stands in relation to your personal reversal model.
7. Modular Indicator Control
You don’t have to use all the indicators. You can enable or disable any of the 12 with a simple checkbox. This means you can build your own “blend” of market context—maybe you only care about RSI, price, and volume. Or maybe you want everything on. The script adapts accordingly, only averaging what you select.
8. Fully Customizable Sensitivity and Lengths
You can adjust the Z-score lookback length globally (default 100), and tweak individual indicator lengths separately. This lets you tune the indicator’s responsiveness to suit your trading style—slower for longer swings, faster for scalping.
9. Clean Integration with Any Chart Layout
All visual elements are designed to be informative without taking over your chart. The coloring is soft but clear, the labels are readable without being huge, and you can turn off any feature you don’t need. The indicator can work as a full dashboard or as a simple line with a couple of alerts—it’s up to you.
10. Precise, Real-Time Signal Logic
The crossover logic for signals is exact and only fires when the Z-score moves across your defined boundary. No estimation, no delay. Everything is calculated based on current and previous bar data, and nothing repaints or back-adjusts.
Conclusion
The Universal Z-Score Valuation indicator is a tool for traders who want a clear, unbiased way to detect overextension. Instead of relying on a single signal, you get a composite of several market perspectives—momentum, volatility, volume, and more—all standardized into a single view. The script gives you the freedom to control the logic, the visuals, and the components. Whether you use it as a confirmation tool or a primary signal source, it’s designed to give you clarity when markets become chaotic.
Disclaimer
This indicator is for research and educational use only. It does not constitute financial advice or guarantees of performance. All trading involves risk, and users should test any strategy thoroughly before applying it to live markets. Use this tool at your own discretion.
Quantum State Superposition Indicator (QSSI)Quantum State Superposition Indicator (QSSI) - Where Physics Meets Finance
The Quantum Revolution in Market Analysis
After months of research into quantum mechanics and its applications to financial markets, I'm thrilled to present the Quantum State Superposition Indicator (QSSI) - a groundbreaking approach that models price action through the lens of quantum physics. This isn't just another technical indicator; it's a paradigm shift in how we understand market behavior.
The Theoretical Foundation
Quantum Superposition in Markets
In quantum mechanics, particles exist in multiple states simultaneously until observed. Similarly, markets exist in a superposition of potential states (bullish, bearish, neutral) until a significant volume event "collapses" the wave function into a definitive direction.
The mathematical framework:
Wave Function (Ψ): Represents the market's quantum state as a weighted sum of all possible states:
Ψ = Σ(αᵢ × Sᵢ)
Where αᵢ are probability amplitudes and Sᵢ are individual quantum states.
Probability Amplitudes: Calculated using the Born rule, normalized so Σ|αᵢ|² = 1
Observation Operator: Volume/Average Volume ratio determines observation strength
The Five Quantum States
Momentum State: Short-term price velocity (EMA of returns)
Mean Reversion State: Deviation from equilibrium (normalized z-score)
Volatility Expansion State: ATR relative to historical average
Trend Continuation State: Long-term price positioning
Chaos State: Volatility of volatility (market uncertainty)
Each state contributes to the overall wave function based on current market conditions.
Wave Function Collapse
When volume exceeds the observation threshold (default 1.5x average), the wave function "collapses," committing the market to a direction. This models how institutional volume forces markets out of uncertainty into trending states.
Collapse Detection Formula:
Collapse = Volume > (Threshold × Average Volume)
Direction = Sign(Ψ) at collapse moment
Advanced Quantum Concepts
Heisenberg Uncertainty Principle
The indicator calculates market uncertainty as the product of price and momentum
uncertainties:
ΔP × ΔM = ℏ (market uncertainty constant)
This manifests as dynamic uncertainty bands that widen during unstable periods.
Quantum Tunneling
Calculates the probability of price "tunneling" through resistance/support barriers:
P(tunnel) = e^(-2×|barrier_height|×√coherence_length)
Unlike classical technical analysis, this gives probability of breakouts before they occur.
Entanglement
Measures the quantum correlation between price and volume:
Entanglement = |Correlation(Price, Volume, lookback)|
High entanglement suggests coordinated institutional activity.
Decoherence
When market states lose quantum properties and behave classically:
Decoherence = 1 - Σ(amplitude²)
Indicates trend emergence from quantum uncertainty.
Visual Innovation
Probability Clouds
Three-tier probability distributions visualize market uncertainty:
Inner Cloud (68%): One standard deviation - most likely price range
Middle Cloud (95%): Two standard deviations - probable extremes
Outer Cloud (99.7%): Three standard deviations - tail risk zones
Cloud width directly represents market uncertainty - wider clouds signal higher entropy states.
Quantum State Visualization
Colored dots represent individual quantum states:
Green: Momentum state strength
Red: Mean reversion state strength
Yellow: Volatility state strength
Dot brightness indicates amplitude (influence) of each state.
Collapse Events
Aqua Diamonds (Above): Bullish collapse - upward commitment
Pink Diamonds (Below): Bearish collapse - downward commitment
These mark precise moments when markets exit superposition.
Implementation Details
Core Calculations
Feature Extraction: Normalize price returns, volume ratios, and volatility measures
State Calculation: Compute each quantum state's value
Amplitude Assignment: Weight states by market conditions and observation strength
Wave Function: Sum weighted states for final market quantum state
Visualization: Transform quantum values to price space for display
Performance Optimization
- Efficient array operations for state calculations
- Single-pass normalization algorithms
- Optimized correlation calculations for entanglement
- Smart label management to prevent visual clutter
Trading Applications:
Signal Generation
Bullish Signals:
- Positive wave function during collapse
- High tunneling probability at support
- Coherent market state with bullish bias
Bearish Signals:
- Negative wave function during collapse
- High tunneling probability at resistance
- Decoherent state transitioning bearish
Risk Management
Uncertainty-Based Position Sizing:
Narrow clouds: Normal position size
Wide clouds: Reduced position size
Extreme uncertainty: Stay flat
Quantum Stop Losses:
- Place stops outside probability clouds
- Adjust for Heisenberg uncertainty
- Respect quantum tunneling levels
Market Regime Recognition
Quantum Coherent (Superposed):
- Market in multiple states
- Avoid directional trades
- Prepare for collapse
Quantum Decoherent (Classical):
-Clear trend emergence
- Follow directional signals
- Traditional analysis applies
Advanced Features
Adaptive Dashboards
Quantum State Panel: Real-time wave function, dominant state, and coherence status
Performance Metrics: Win rate, signal frequency, and regime analysis
Information Guide: Comprehensive explanation of all quantum concepts
- All dashboards feature adjustable sizing for different screen resolutions.
Multi-Timeframe Quantum Analysis
The indicator adapts to any timeframe:
Scalping (1-5m): Short coherence length, sensitive thresholds
Day Trading (15m-1H): Balanced parameters
Swing Trading (4H-1D): Long coherence, stable states
Alert System
Sophisticated alerts for:
- Wave function collapse events
- Decoherence transitions
- High tunneling probability
- Strong entanglement detection
Originality & Innovation
This indicator introduces several firsts:
Quantum Superposition: First to model markets as quantum systems
Wave Function Collapse: Original volume-triggered state commitment
Tunneling Probability: Novel breakout prediction method
Entanglement Metrics: Unique price-volume quantum correlation
Probability Clouds: Revolutionary uncertainty visualization
Development Journey
Creating QSSI required:
- Deep study of quantum mechanics principles
- Translation of physics equations to market context
- Extensive backtesting across multiple markets
- UI/UX optimization for trader accessibility
- Performance optimization for real-time calculation
- The result bridges cutting-edge physics with practical trading.
Best Practices
Parameter Optimization
Quantum States (2-5):
- 2-3 for simple markets (forex majors)
- 4-5 for complex markets (indices, crypto)
Coherence Length (10-50):
- Lower for fast markets
- Higher for stable markets
Observation Threshold (1.0-3.0):
- Lower for active markets
- Higher for thin markets
Signal Confirmation
Always confirm quantum signals with:
- Market structure (support/resistance)
- Volume patterns
- Correlated assets
- Fundamental context
Risk Guidelines
- Never risk more than 2% per trade
- Respect probability cloud boundaries
- Exit on decoherence shifts
- Scale with confidence levels
Educational Value
QSSI teaches advanced concepts:
- Quantum mechanics applications
- Probability theory
- Non-linear dynamics
- Risk management
- Market microstructure
Perfect for traders seeking deeper market understanding.
Disclaimer
This indicator is for educational and research purposes only. While quantum mechanics provides a fascinating framework for market analysis, no indicator can predict future prices with certainty. The probabilistic nature of both quantum mechanics and markets means outcomes are inherently uncertain.
Always use proper risk management, conduct thorough analysis, and never risk more than you can afford to lose. Past performance does not guarantee future results.
Conclusion
The Quantum State Superposition Indicator represents a revolutionary approach to market analysis, bringing institutional-grade quantum modeling to retail traders. By viewing markets through the lens of quantum mechanics, we gain unique insights into uncertainty, probability, and state transitions that classical indicators miss.
Whether you're a physicist interested in finance or a trader seeking cutting-edge tools, QSSI opens new dimensions in market analysis.
"The market, like Schrödinger's cat, exists in multiple states until observed through volume."
* As you may have noticed, the past two indicators I've released (Lorentzian Classification and Quantum State Superposition) are designed with strategy implementation in mind. I'm currently developing a stable execution platform that's completely unique and moves away from traditional ATR-based position sizing and stop loss systems. I've found ATR-based approaches to be unreliable in volatile markets and regime transitions - they often lag behind actual market conditions and can lead to premature exits or oversized positions during volatility spikes.
The goal is to create something that adapts to market conditions in real-time using the quantum and relativistic principles we've been exploring. Hopefully I'll have something groundbreaking to share soon. Stay tuned!
Trade with quantum insight. Trade with QSSI .
— Dskyz , for DAFE Trading Systems
Topological Market Stress (TMS) - Quantum FabricTopological Market Stress (TMS) - Quantum Fabric
What Stresses The Market?
Topological Market Stress (TMS) represents a revolutionary fusion of algebraic topology and quantum field theory applied to financial markets. Unlike traditional indicators that analyze price movements linearly, TMS examines the underlying topological structure of market data—detecting when the very fabric of market relationships begins to tear, warp, or collapse.
Drawing inspiration from the ethereal beauty of quantum field visualizations and the mathematical elegance of topological spaces, this indicator transforms complex mathematical concepts into an intuitive, visually stunning interface that reveals hidden market dynamics invisible to conventional analysis.
Theoretical Foundation: Topology Meets Markets
Topological Holes in Market Structure
In algebraic topology, a "hole" represents a fundamental structural break—a place where the normal connectivity of space fails. In markets, these topological holes manifest as:
Correlation Breakdown: When traditional price-volume relationships collapse
Volatility Clustering Failure: When volatility patterns lose their predictive power
Microstructure Stress: When market efficiency mechanisms begin to fail
The Mathematics of Market Topology
TMS constructs a topological space from market data using three key components:
1. Correlation Topology
ρ(P,V) = correlation(price, volume, period)
Hole Formation = 1 - |ρ(P,V)|
When price and volume decorrelate, topological holes begin forming.
2. Volatility Clustering Topology
σ(t) = volatility at time t
Clustering = correlation(σ(t), σ(t-1), period)
Breakdown = 1 - |Clustering|
Volatility clustering breakdown indicates structural instability.
3. Market Efficiency Topology
Efficiency = |price - EMA(price)| / ATR
Measures how far price deviates from its efficient trajectory.
Multi-Scale Topological Analysis
Markets exist across multiple temporal scales simultaneously. TMS analyzes topology at three distinct scales:
Micro Scale (3-15 periods): Immediate structural changes, market microstructure stress
Meso Scale (10-50 periods): Trend-level topology, medium-term structural shifts
Macro Scale (50-200 periods): Long-term structural topology, regime-level changes
The final stress metric combines all scales:
Combined Stress = 0.3×Micro + 0.4×Meso + 0.3×Macro
How TMS Works
1. Topological Space Construction
Each market moment is embedded in a multi-dimensional topological space where:
- Price efficiency forms one dimension
- Correlation breakdown forms another
- Volatility clustering breakdown forms the third
2. Hole Detection Algorithm
The indicator continuously scans this topological space for:
Hole Formation: When stress exceeds the formation threshold
Hole Persistence: How long structural breaks maintain
Hole Collapse: Sudden topology restoration (regime shifts)
3. Quantum Visualization Engine
The visualization system translates topological mathematics into intuitive quantum field representations:
Stress Waves: Main line showing topological stress intensity
Quantum Glow: Surrounding field indicating stress energy
Fabric Integrity: Background showing structural health
Multi-Scale Rings: Orbital representations of different timeframes
4. Signal Generation
Stable Topology (✨): Normal market structure, standard trading conditions
Stressed Topology (⚡): Increased structural tension, heightened volatility expected
Topological Collapse (🕳️): Major structural break, regime shift in progress
Critical Stress (🌋): Extreme conditions, maximum caution required
Inputs & Parameters
🕳️ Topological Parameters
Analysis Window (20-200, default: 50)
Primary period for topological analysis
20-30: High-frequency scalping, rapid structure detection
50: Balanced approach, recommended for most markets
100-200: Long-term position trading, major structural shifts only
Hole Formation Threshold (0.1-0.9, default: 0.3)
Sensitivity for detecting topological holes
0.1-0.2: Very sensitive, detects minor structural stress
0.3: Balanced, optimal for most market conditions
0.5-0.9: Conservative, only major structural breaks
Density Calculation Radius (0.1-2.0, default: 0.5)
Radius for local density estimation in topological space
0.1-0.3: Fine-grained analysis, sensitive to local changes
0.5: Standard approach, balanced sensitivity
1.0-2.0: Broad analysis, focuses on major structural features
Collapse Detection (0.5-0.95, default: 0.7)
Threshold for detecting sudden topology restoration
0.5-0.6: Very sensitive to regime changes
0.7: Balanced, reliable collapse detection
0.8-0.95: Conservative, only major regime shifts
📊 Multi-Scale Analysis
Enable Multi-Scale (default: true)
- Analyzes topology across multiple timeframes simultaneously
- Provides deeper insight into market structure at different scales
- Essential for understanding cross-timeframe topology interactions
Micro Scale Period (3-15, default: 5)
Fast scale for immediate topology changes
3-5: Ultra-fast, tick/minute data analysis
5-8: Fast, 5m-15m chart optimization
10-15: Medium-fast, 30m-1H chart focus
Meso Scale Period (10-50, default: 20)
Medium scale for trend topology analysis
10-15: Short trend structures
20-25: Medium trend structures (recommended)
30-50: Long trend structures
Macro Scale Period (50-200, default: 100)
Slow scale for structural topology
50-75: Medium-term structural analysis
100: Long-term structure (recommended)
150-200: Very long-term structural patterns
⚙️ Signal Processing
Smoothing Method (SMA/EMA/RMA/WMA, default: EMA) Method for smoothing stress signals
SMA: Simple average, stable but slower
EMA: Exponential, responsive and recommended
RMA: Running average, very smooth
WMA: Weighted average, balanced approach
Smoothing Period (1-10, default: 3)
Period for signal smoothing
1-2: Minimal smoothing, noisy but fast
3-5: Balanced, recommended for most applications
6-10: Heavy smoothing, slow but very stable
Normalization (Fixed/Adaptive/Rolling, default: Adaptive)
Method for normalizing stress values
Fixed: Static 0-1 range normalization
Adaptive: Dynamic range adjustment (recommended)
Rolling: Rolling window normalization
🎨 Quantum Visualization
Fabric Style Options:
Quantum Field: Flowing energy visualization with smooth gradients
Topological Mesh: Mathematical topology with stepped lines
Phase Space: Dynamical systems view with circular markers
Minimal: Clean, simple display with reduced visual elements
Color Scheme Options:
Quantum Gradient: Deep space blue → Quantum red progression
Thermal: Black → Hot orange thermal imaging style
Spectral: Purple → Gold full spectrum colors
Monochrome: Dark gray → Light gray elegant simplicity
Multi-Scale Rings (default: true)
- Display orbital rings for different time scales
- Visualizes how topology changes across timeframes
- Provides immediate visual feedback on cross-scale dynamics
Glow Intensity (0.0-1.0, default: 0.6)
Controls the quantum glow effect intensity
0.0: No glow, pure line display
0.6: Balanced, recommended setting
1.0: Maximum glow, full quantum field effect
📋 Dashboard & Alerts
Show Dashboard (default: true)
Real-time topology status display
Current market state and trading recommendations
Stress level visualization and fabric integrity status
Show Theory Guide (default: true)
Educational panel explaining topological concepts
Dashboard interpretation guide
Trading strategy recommendations
Enable Alerts (default: true)
Extreme stress detection alerts
Topological collapse notifications
Hole formation and recovery signals
Visual Logic & Interpretation
Main Visualization Elements
Quantum Stress Line
Primary indicator showing topological stress intensity
Color intensity reflects current market state
Line style varies based on selected fabric style
Glow effect indicates stress energy field
Equilibrium Line
Silver line showing average stress level
Reference point for normal market conditions
Helps identify when stress is elevated or suppressed
Upper/Lower Bounds
Red upper bound: High stress threshold
Green lower bound: Low stress threshold
Quantum fabric fill between bounds shows stress field
Multi-Scale Rings
Aqua circles : Micro-scale topology (immediate changes)
Orange circles: Meso-scale topology (trend-level changes)
Provides cross-timeframe topology visualization
Dashboard Information
Topology State Icons:
✨ STABLE: Normal market structure, standard trading conditions
⚡ STRESSED: Increased structural tension, monitor closely
🕳️ COLLAPSE: Major structural break, regime shift occurring
🌋 CRITICAL: Extreme conditions, reduce risk exposure
Stress Bar Visualization:
Visual representation of current stress level (0-100%)
Color-coded based on current topology state
Real-time percentage display
Fabric Integrity Dots:
●●●●● Intact: Strong market structure (0-30% stress)
●●●○○ Stressed: Weakening structure (30-70% stress)
●○○○○ Fractured: Breaking down structure (70-100% stress)
Action Recommendations:
✅ TRADE: Normal conditions, standard strategies apply
⚠️ WATCH: Monitor closely, increased vigilance required
🔄 ADAPT: Change strategy, regime shift in progress
🛑 REDUCE: Lower risk exposure, extreme conditions
Trading Strategies
In Stable Topology (✨ STABLE)
- Normal trading conditions apply
- Use standard technical analysis
- Regular position sizing appropriate
- Both trend-following and mean-reversion strategies viable
In Stressed Topology (⚡ STRESSED)
- Increased volatility expected
- Widen stop losses to account for higher volatility
- Reduce position sizes slightly
- Focus on high-probability setups
- Monitor for potential regime change
During Topological Collapse (🕳️ COLLAPSE)
- Major regime shift in progress
- Adapt strategy immediately to new market character
- Consider closing positions that rely on previous regime
- Wait for new topology to stabilize before major trades
- Opportunity for contrarian plays if collapse is extreme
In Critical Stress (🌋 CRITICAL)
- Extreme market conditions
- Significantly reduce risk exposure
- Avoid new positions until stress subsides
- Focus on capital preservation
- Consider hedging existing positions
Advanced Techniques
Multi-Timeframe Topology Analysis
- Use higher timeframe TMS for regime context
- Use lower timeframe TMS for precise entry timing
- Alignment across timeframes = highest probability trades
Topology Divergence Trading
- Most powerful at regime boundaries
- Price makes new high/low but topology stress decreases
- Early warning of potential reversals
- Combine with key support/resistance levels
Stress Persistence Analysis
- Long periods of stable topology often precede major moves
- Extended stress periods often resolve in regime changes
- Use persistence tracking for position sizing decisions
Originality & Innovation
TMS represents a genuine breakthrough in applying advanced mathematics to market analysis:
True Topological Analysis: Not a simplified proxy but actual topological space construction and hole detection using correlation breakdown, volatility clustering analysis, and market efficiency measurement.
Quantum Aesthetic: Transforms complex topology mathematics into an intuitive, visually stunning interface inspired by quantum field theory visualizations.
Multi-Scale Architecture: Simultaneous analysis across micro, meso, and macro timeframes provides unprecedented insight into market structure dynamics.
Regime Detection: Identifies fundamental market character changes before they become obvious in price action, providing early warning of structural shifts.
Practical Application: Clear, actionable signals derived from advanced mathematical concepts, making theoretical topology accessible to practical traders.
This is not a combination of existing indicators or a cosmetic enhancement of standard tools. It represents a fundamental reimagining of how we measure, visualize, and interpret market dynamics through the lens of algebraic topology and quantum field theory.
Best Practices
Start with defaults: Parameters are optimized for broad market applicability
Match timeframe: Adjust scales based on your trading timeframe
Confirm with price action: TMS shows market character, not direction
Respect topology changes: Reduce risk during regime transitions
Use appropriate strategies: Adapt approach based on current topology state
Monitor persistence: Track how long topology states maintain
Cross-timeframe analysis: Align multiple timeframes for highest probability trades
Alerts Available
Extreme Topological Stress: Market fabric under severe deformation
Topological Collapse Detected: Regime shift in progress
Topological Hole Forming: Market structure breakdown detected
Topology Stabilizing: Market structure recovering to normal
Chart Requirements
Recommended Markets: All liquid markets (forex, stocks, crypto, futures)
Optimal Timeframes: 5m to Daily (adaptable to any timeframe)
Minimum History: 200 bars for proper topology construction
Best Performance: Markets with clear regime characteristics
Academic Foundation
This indicator draws from cutting-edge research in:
- Algebraic topology and persistent homology
- Quantum field theory visualization techniques
- Market microstructure analysis
- Multi-scale dynamical systems theory
- Correlation topology and network analysis
Disclaimer
This indicator is for educational and research purposes only. It does not constitute financial advice or provide direct buy/sell signals. Topological analysis reveals market structure characteristics, not future price direction. Always use proper risk management and combine with your own analysis. Past performance does not guarantee future results.
See markets through the lens of topology. Trade the structure, not the noise.
Bringing advanced mathematics to practical trading through quantum-inspired visualization.
Trade with insight. Trade with structure.
— Dskyz , for DAFE Trading Systems
Lorentzian Classification - Advanced Trading DashboardLorentzian Classification - Relativistic Market Analysis
A Journey from Theory to Trading Reality
What began as fascination with Einstein's relativity and Lorentzian geometry has evolved into a practical trading tool that bridges theoretical physics and market dynamics. This indicator represents months of wrestling with complex mathematical concepts, debugging intricate algorithms, and transforming abstract theory into actionable trading signals.
The Theoretical Foundation
Lorentzian Distance in Market Space
Traditional Euclidean distance treats all feature differences equally, but markets don't behave uniformly. Lorentzian distance, borrowed from spacetime geometry, provides a more nuanced similarity measure:
d(x,y) = Σ ln(1 + |xi - yi|)
This logarithmic formulation naturally handles:
Scale invariance: Large price moves don't overwhelm small but significant patterns
Outlier robustness: Extreme values are dampened rather than dominating
Non-linear relationships: Captures market behavior better than linear metrics
K-Nearest Neighbors with Relativistic Weighting
The algorithm searches historical market states for patterns similar to current conditions. Each neighbor receives weight inversely proportional to its Lorentzian distance:
w = 1 / (1 + distance)
This creates a "gravitational" effect where closer patterns have stronger influence on predictions.
The Implementation Challenge
Creating meaningful market features required extensive experimentation:
Price Features: Multi-timeframe momentum (1, 2, 3, 5, 8 bar lookbacks) Volume Features: Relative volume analysis against 20-period average
Volatility Features: ATR and Bollinger Band width normalization Momentum Features: RSI deviation from neutral and MACD/price ratio
Each feature undergoes min-max normalization to ensure equal weighting in distance calculations.
The Prediction Mechanism
For each current market state:
Feature Vector Construction: 12-dimensional representation of market conditions
Historical Search: Scan lookback period for similar patterns using Lorentzian distance
Neighbor Selection: Identify K nearest historical matches
Outcome Analysis: Examine what happened N bars after each match
Weighted Prediction: Combine outcomes using distance-based weights
Confidence Calculation: Measure agreement between neighbors
Technical Hurdles Overcome
Array Management: Complex indexing to prevent look-ahead bias
Distance Calculations: Optimizing nested loops for performance
Memory Constraints: Balancing lookback depth with computational limits
Signal Filtering: Preventing clustering of identical signals
Advanced Dashboard System
Main Control Panel
The primary dashboard provides real-time market intelligence:
Signal Status: Current prediction with confidence percentage
Neighbor Analysis: How many historical patterns match current conditions
Market Regime: Trend strength, volatility, and volume analysis
Temporal Context: Real-time updates with timestamp
Performance Analytics
Comprehensive tracking system monitors:
Win Rate: Percentage of successful predictions
Signal Count: Total predictions generated
Streak Analysis: Current winning/losing sequence
Drawdown Monitoring: Maximum equity decline
Sharpe Approximation: Risk-adjusted performance estimate
Risk Assessment Panel
Multi-dimensional risk analysis:
RSI Positioning: Overbought/oversold conditions
ATR Percentage: Current volatility relative to price
Bollinger Position: Price location within volatility bands
MACD Alignment: Momentum confirmation
Confidence Heatmap
Visual representation of prediction reliability:
Historical Confidence: Last 10 periods of prediction certainty
Strength Analysis: Magnitude of prediction values over time
Pattern Recognition: Color-coded confidence levels for quick assessment
Input Parameters Deep Dive
Core Algorithm Settings
K Nearest Neighbors (1-20): More neighbors create smoother but less responsive signals. Optimal range 5-8 for most markets.
Historical Lookback (50-500): Deeper history improves pattern recognition but reduces adaptability. 100-200 bars optimal for most timeframes.
Feature Window (5-30): Longer windows capture more context but reduce sensitivity. Match to your trading timeframe.
Feature Selection
Price Changes: Essential for momentum and reversal detection Volume Profile: Critical for institutional activity recognition Volatility Measures: Key for regime change detection Momentum Indicators: Vital for trend confirmation
Signal Generation
Prediction Horizon (1-20): How far ahead to predict. Shorter horizons for scalping, longer for swing trading.
Signal Threshold (0.5-0.9): Confidence required for signal generation. Higher values reduce false signals but may miss opportunities.
Smoothing (1-10): EMA applied to raw predictions. More smoothing reduces noise but increases lag.
Visual Design Philosophy
Color Themes
Professional: Corporate blue/red for institutional environments Neon: Cyberpunk cyan/magenta for modern aesthetics
Matrix: Green/red hacker-inspired palette Classic: Traditional trading colors
Information Hierarchy
The dashboard system prioritizes information by importance:
Primary Signals: Largest, most prominent display
Confidence Metrics: Secondary but clearly visible
Supporting Data: Detailed but unobtrusive
Historical Context: Available but not distracting
Trading Applications
Signal Interpretation
Long Signals: Prediction > threshold with high confidence
Look for volume confirmation
- Check trend alignment
- Verify support levels
Short Signals: Prediction < -threshold with high confidence
Confirm with resistance levels
- Check for distribution patterns
- Verify momentum divergence
- Market Regime Adaptation
Trending Markets: Higher confidence in directional signals
Ranging Markets: Focus on reversal signals at extremes
Volatile Markets: Require higher confidence thresholds
Low Volume: Reduce position sizes, increase caution
Risk Management Integration
Confidence-Based Sizing: Larger positions for higher confidence signals
Regime-Aware Stops: Wider stops in volatile regimes
Multi-Timeframe Confirmation: Align signals across timeframes
Volume Confirmation: Require volume support for major signals
Originality and Innovation
This indicator represents genuine innovation in several areas:
Mathematical Approach
First application of Lorentzian geometry to market pattern recognition. Unlike Euclidean-based systems, this naturally handles market non-linearities.
Feature Engineering
Sophisticated multi-dimensional feature space combining price, volume, volatility, and momentum in normalized form.
Visualization System
Professional-grade dashboard system providing comprehensive market intelligence in intuitive format.
Performance Tracking
Real-time performance analytics typically found only in institutional trading systems.
Development Journey
Creating this indicator involved overcoming numerous technical challenges:
Mathematical Complexity: Translating theoretical concepts into practical code
Performance Optimization: Balancing accuracy with computational efficiency
User Interface Design: Making complex data accessible and actionable
Signal Quality: Filtering noise while maintaining responsiveness
The result is a tool that brings institutional-grade analytics to individual traders while maintaining the theoretical rigor of its mathematical foundation.
Best Practices
- Parameter Optimization
- Start with default settings and adjust based on:
Market Characteristics: Volatile vs. stable
Trading Timeframe: Scalping vs. swing trading
Risk Tolerance: Conservative vs. aggressive
Signal Confirmation
Never trade on Lorentzian signals alone:
Price Action: Confirm with support/resistance
Volume: Verify with volume analysis
Multiple Timeframes: Check higher timeframe alignment
Market Context: Consider overall market conditions
Risk Management
Position Sizing: Scale with confidence levels
Stop Losses: Adapt to market volatility
Profit Targets: Based on historical performance
Maximum Risk: Never exceed 2-3% per trade
Disclaimer
This indicator is for educational and research purposes only. It does not constitute financial advice or guarantee profitable trading results. The Lorentzian classification system reveals market patterns but cannot predict future price movements with certainty. Always use proper risk management, conduct your own analysis, and never risk more than you can afford to lose.
Market dynamics are inherently uncertain, and past performance does not guarantee future results. This tool should be used as part of a comprehensive trading strategy, not as a standalone solution.
Bringing the elegance of relativistic geometry to market analysis through sophisticated pattern recognition and intuitive visualization.
Thank you for sharing the idea. You're more than a follower, you're a leader!
@vasanthgautham1221
Trade with precision. Trade with insight.
— Dskyz , for DAFE Trading Systems
