Quantum Rotational Field MappingQuantum Rotational Field Mapping (QRFM):
Phase Coherence Detection Through Complex-Plane Oscillator Analysis
Quantum Rotational Field Mapping applies complex-plane mathematics and phase-space analysis to oscillator ensembles, identifying high-probability trend ignition points by measuring when multiple independent oscillators achieve phase coherence. Unlike traditional multi-oscillator approaches that simply stack indicators or use boolean AND/OR logic, this system converts each oscillator into a rotating phasor (vector) in the complex plane and calculates the Coherence Index (CI) —a mathematical measure of how tightly aligned the ensemble has become—then generates signals only when alignment, phase direction, and pairwise entanglement all converge.
The indicator combines three mathematical frameworks: phasor representation using analytic signal theory to extract phase and amplitude from each oscillator, coherence measurement using vector summation in the complex plane to quantify group alignment, and entanglement analysis that calculates pairwise phase agreement across all oscillator combinations. This creates a multi-dimensional confirmation system that distinguishes between random oscillator noise and genuine regime transitions.
What Makes This Original
Complex-Plane Phasor Framework
This indicator implements classical signal processing mathematics adapted for market oscillators. Each oscillator—whether RSI, MACD, Stochastic, CCI, Williams %R, MFI, ROC, or TSI—is first normalized to a common scale, then converted into a complex-plane representation using an in-phase (I) and quadrature (Q) component. The in-phase component is the oscillator value itself, while the quadrature component is calculated as the first difference (derivative proxy), creating a velocity-aware representation.
From these components, the system extracts:
Phase (φ) : Calculated as φ = atan2(Q, I), representing the oscillator's position in its cycle (mapped to -180° to +180°)
Amplitude (A) : Calculated as A = √(I² + Q²), representing the oscillator's strength or conviction
This mathematical approach is fundamentally different from simply reading oscillator values. A phasor captures both where an oscillator is in its cycle (phase angle) and how strongly it's expressing that position (amplitude). Two oscillators can have the same value but be in opposite phases of their cycles—traditional analysis would see them as identical, while QRFM sees them as 180° out of phase (contradictory).
Coherence Index Calculation
The core innovation is the Coherence Index (CI) , borrowed from physics and signal processing. When you have N oscillators, each with phase φₙ, you can represent each as a unit vector in the complex plane: e^(iφₙ) = cos(φₙ) + i·sin(φₙ).
The CI measures what happens when you sum all these vectors:
Resultant Vector : R = Σ e^(iφₙ) = Σ cos(φₙ) + i·Σ sin(φₙ)
Coherence Index : CI = |R| / N
Where |R| is the magnitude of the resultant vector and N is the number of active oscillators.
The CI ranges from 0 to 1:
CI = 1.0 : Perfect coherence—all oscillators have identical phase angles, vectors point in the same direction, creating maximum constructive interference
CI = 0.0 : Complete decoherence—oscillators are randomly distributed around the circle, vectors cancel out through destructive interference
0 < CI < 1 : Partial alignment—some clustering with some scatter
This is not a simple average or correlation. The CI captures phase synchronization across the entire ensemble simultaneously. When oscillators phase-lock (align their cycles), the CI spikes regardless of their individual values. This makes it sensitive to regime transitions that traditional indicators miss.
Dominant Phase and Direction Detection
Beyond measuring alignment strength, the system calculates the dominant phase of the ensemble—the direction the resultant vector points:
Dominant Phase : φ_dom = atan2(Σ sin(φₙ), Σ cos(φₙ))
This gives the "average direction" of all oscillator phases, mapped to -180° to +180°:
+90° to -90° (right half-plane): Bullish phase dominance
+90° to +180° or -90° to -180° (left half-plane): Bearish phase dominance
The combination of CI magnitude (coherence strength) and dominant phase angle (directional bias) creates a two-dimensional signal space. High CI alone is insufficient—you need high CI plus dominant phase pointing in a tradeable direction. This dual requirement is what separates QRFM from simple oscillator averaging.
Entanglement Matrix and Pairwise Coherence
While the CI measures global alignment, the entanglement matrix measures local pairwise relationships. For every pair of oscillators (i, j), the system calculates:
E(i,j) = |cos(φᵢ - φⱼ)|
This represents the phase agreement between oscillators i and j:
E = 1.0 : Oscillators are in-phase (0° or 360° apart)
E = 0.0 : Oscillators are in quadrature (90° apart, orthogonal)
E between 0 and 1 : Varying degrees of alignment
The system counts how many oscillator pairs exceed a user-defined entanglement threshold (e.g., 0.7). This entangled pairs count serves as a confirmation filter: signals require not just high global CI, but also a minimum number of strong pairwise agreements. This prevents false ignitions where CI is high but driven by only two oscillators while the rest remain scattered.
The entanglement matrix creates an N×N symmetric matrix that can be visualized as a web—when many cells are bright (high E values), the ensemble is highly interconnected. When cells are dark, oscillators are moving independently.
Phase-Lock Tolerance Mechanism
A complementary confirmation layer is the phase-lock detector . This calculates the maximum phase spread across all oscillators:
For all pairs (i,j), compute angular distance: Δφ = |φᵢ - φⱼ|, wrapping at 180°
Max Spread = maximum Δφ across all pairs
If max spread < user threshold (e.g., 35°), the ensemble is considered phase-locked —all oscillators are within a narrow angular band.
This differs from entanglement: entanglement measures pairwise cosine similarity (magnitude of alignment), while phase-lock measures maximum angular deviation (tightness of clustering). Both must be satisfied for the highest-conviction signals.
Multi-Layer Visual Architecture
QRFM includes six visual components that represent the same underlying mathematics from different perspectives:
Circular Orbit Plot : A polar coordinate grid showing each oscillator as a vector from origin to perimeter. Angle = phase, radius = amplitude. This is a real-time snapshot of the complex plane. When vectors converge (point in similar directions), coherence is high. When scattered randomly, coherence is low. Users can see phase alignment forming before CI numerically confirms it.
Phase-Time Heat Map : A 2D matrix with rows = oscillators and columns = time bins. Each cell is colored by the oscillator's phase at that time (using a gradient where color hue maps to angle). Horizontal color bands indicate sustained phase alignment over time. Vertical color bands show moments when all oscillators shared the same phase (ignition points). This provides historical pattern recognition.
Entanglement Web Matrix : An N×N grid showing E(i,j) for all pairs. Cells are colored by entanglement strength—bright yellow/gold for high E, dark gray for low E. This reveals which oscillators are driving coherence and which are lagging. For example, if RSI and MACD show high E but Stochastic shows low E with everything, Stochastic is the outlier.
Quantum Field Cloud : A background color overlay on the price chart. Color (green = bullish, red = bearish) is determined by dominant phase. Opacity is determined by CI—high CI creates dense, opaque cloud; low CI creates faint, nearly invisible cloud. This gives an atmospheric "feel" for regime strength without looking at numbers.
Phase Spiral : A smoothed plot of dominant phase over recent history, displayed as a curve that wraps around price. When the spiral is tight and rotating steadily, the ensemble is in coherent rotation (trending). When the spiral is loose or erratic, coherence is breaking down.
Dashboard : A table showing real-time metrics: CI (as percentage), dominant phase (in degrees with directional arrow), field strength (CI × average amplitude), entangled pairs count, phase-lock status (locked/unlocked), quantum state classification ("Ignition", "Coherent", "Collapse", "Chaos"), and collapse risk (recent CI change normalized to 0-100%).
Each component is independently toggleable, allowing users to customize their workspace. The orbit plot is the most essential—it provides intuitive, visual feedback on phase alignment that no numerical dashboard can match.
Core Components and How They Work Together
1. Oscillator Normalization Engine
The foundation is creating a common measurement scale. QRFM supports eight oscillators:
RSI : Normalized from to using overbought/oversold levels (70, 30) as anchors
MACD Histogram : Normalized by dividing by rolling standard deviation, then clamped to
Stochastic %K : Normalized from using (80, 20) anchors
CCI : Divided by 200 (typical extreme level), clamped to
Williams %R : Normalized from using (-20, -80) anchors
MFI : Normalized from using (80, 20) anchors
ROC : Divided by 10, clamped to
TSI : Divided by 50, clamped to
Each oscillator can be individually enabled/disabled. Only active oscillators contribute to phase calculations. The normalization removes scale differences—a reading of +0.8 means "strongly bullish" regardless of whether it came from RSI or TSI.
2. Analytic Signal Construction
For each active oscillator at each bar, the system constructs the analytic signal:
In-Phase (I) : The normalized oscillator value itself
Quadrature (Q) : The bar-to-bar change in the normalized value (first derivative approximation)
This creates a 2D representation: (I, Q). The phase is extracted as:
φ = atan2(Q, I) × (180 / π)
This maps the oscillator to a point on the unit circle. An oscillator at the same value but rising (positive Q) will have a different phase than one that is falling (negative Q). This velocity-awareness is critical—it distinguishes between "at resistance and stalling" versus "at resistance and breaking through."
The amplitude is extracted as:
A = √(I² + Q²)
This represents the distance from origin in the (I, Q) plane. High amplitude means the oscillator is far from neutral (strong conviction). Low amplitude means it's near zero (weak/transitional state).
3. Coherence Calculation Pipeline
For each bar (or every Nth bar if phase sample rate > 1 for performance):
Step 1 : Extract phase φₙ for each of the N active oscillators
Step 2 : Compute complex exponentials: Zₙ = e^(i·φₙ·π/180) = cos(φₙ·π/180) + i·sin(φₙ·π/180)
Step 3 : Sum the complex exponentials: R = Σ Zₙ = (Σ cos φₙ) + i·(Σ sin φₙ)
Step 4 : Calculate magnitude: |R| = √
Step 5 : Normalize by count: CI_raw = |R| / N
Step 6 : Smooth the CI: CI = SMA(CI_raw, smoothing_window)
The smoothing step (default 2 bars) removes single-bar noise spikes while preserving structural coherence changes. Users can adjust this to control reactivity versus stability.
The dominant phase is calculated as:
φ_dom = atan2(Σ sin φₙ, Σ cos φₙ) × (180 / π)
This is the angle of the resultant vector R in the complex plane.
4. Entanglement Matrix Construction
For all unique pairs of oscillators (i, j) where i < j:
Step 1 : Get phases φᵢ and φⱼ
Step 2 : Compute phase difference: Δφ = φᵢ - φⱼ (in radians)
Step 3 : Calculate entanglement: E(i,j) = |cos(Δφ)|
Step 4 : Store in symmetric matrix: matrix = matrix = E(i,j)
The matrix is then scanned: count how many E(i,j) values exceed the user-defined threshold (default 0.7). This count is the entangled pairs metric.
For visualization, the matrix is rendered as an N×N table where cell brightness maps to E(i,j) intensity.
5. Phase-Lock Detection
Step 1 : For all unique pairs (i, j), compute angular distance: Δφ = |φᵢ - φⱼ|
Step 2 : Wrap angles: if Δφ > 180°, set Δφ = 360° - Δφ
Step 3 : Find maximum: max_spread = max(Δφ) across all pairs
Step 4 : Compare to tolerance: phase_locked = (max_spread < tolerance)
If phase_locked is true, all oscillators are within the specified angular cone (e.g., 35°). This is a boolean confirmation filter.
6. Signal Generation Logic
Signals are generated through multi-layer confirmation:
Long Ignition Signal :
CI crosses above ignition threshold (e.g., 0.80)
AND dominant phase is in bullish range (-90° < φ_dom < +90°)
AND phase_locked = true
AND entangled_pairs >= minimum threshold (e.g., 4)
Short Ignition Signal :
CI crosses above ignition threshold
AND dominant phase is in bearish range (φ_dom < -90° OR φ_dom > +90°)
AND phase_locked = true
AND entangled_pairs >= minimum threshold
Collapse Signal :
CI at bar minus CI at current bar > collapse threshold (e.g., 0.55)
AND CI at bar was above 0.6 (must collapse from coherent state, not from already-low state)
These are strict conditions. A high CI alone does not generate a signal—dominant phase must align with direction, oscillators must be phase-locked, and sufficient pairwise entanglement must exist. This multi-factor gating dramatically reduces false signals compared to single-condition triggers.
Calculation Methodology
Phase 1: Oscillator Computation and Normalization
On each bar, the system calculates the raw values for all enabled oscillators using standard Pine Script functions:
RSI: ta.rsi(close, length)
MACD: ta.macd() returning histogram component
Stochastic: ta.stoch() smoothed with ta.sma()
CCI: ta.cci(close, length)
Williams %R: ta.wpr(length)
MFI: ta.mfi(hlc3, length)
ROC: ta.roc(close, length)
TSI: ta.tsi(close, short, long)
Each raw value is then passed through a normalization function:
normalize(value, overbought_level, oversold_level) = 2 × (value - oversold) / (overbought - oversold) - 1
This maps the oscillator's typical range to , where -1 represents extreme bearish, 0 represents neutral, and +1 represents extreme bullish.
For oscillators without fixed ranges (MACD, ROC, TSI), statistical normalization is used: divide by a rolling standard deviation or fixed divisor, then clamp to .
Phase 2: Phasor Extraction
For each normalized oscillator value val:
I = val (in-phase component)
Q = val - val (quadrature component, first difference)
Phase calculation:
phi_rad = atan2(Q, I)
phi_deg = phi_rad × (180 / π)
Amplitude calculation:
A = √(I² + Q²)
These values are stored in arrays: osc_phases and osc_amps for each oscillator n.
Phase 3: Complex Summation and Coherence
Initialize accumulators:
sum_cos = 0
sum_sin = 0
For each oscillator n = 0 to N-1:
phi_rad = osc_phases × (π / 180)
sum_cos += cos(phi_rad)
sum_sin += sin(phi_rad)
Resultant magnitude:
resultant_mag = √(sum_cos² + sum_sin²)
Coherence Index (raw):
CI_raw = resultant_mag / N
Smoothed CI:
CI = SMA(CI_raw, smoothing_window)
Dominant phase:
phi_dom_rad = atan2(sum_sin, sum_cos)
phi_dom_deg = phi_dom_rad × (180 / π)
Phase 4: Entanglement Matrix Population
For i = 0 to N-2:
For j = i+1 to N-1:
phi_i = osc_phases × (π / 180)
phi_j = osc_phases × (π / 180)
delta_phi = phi_i - phi_j
E = |cos(delta_phi)|
matrix_index_ij = i × N + j
matrix_index_ji = j × N + i
entangle_matrix = E
entangle_matrix = E
if E >= threshold:
entangled_pairs += 1
The matrix uses flat array storage with index mapping: index(row, col) = row × N + col.
Phase 5: Phase-Lock Check
max_spread = 0
For i = 0 to N-2:
For j = i+1 to N-1:
delta = |osc_phases - osc_phases |
if delta > 180:
delta = 360 - delta
max_spread = max(max_spread, delta)
phase_locked = (max_spread < tolerance)
Phase 6: Signal Evaluation
Ignition Long :
ignition_long = (CI crosses above threshold) AND
(phi_dom > -90 AND phi_dom < 90) AND
phase_locked AND
(entangled_pairs >= minimum)
Ignition Short :
ignition_short = (CI crosses above threshold) AND
(phi_dom < -90 OR phi_dom > 90) AND
phase_locked AND
(entangled_pairs >= minimum)
Collapse :
CI_prev = CI
collapse = (CI_prev - CI > collapse_threshold) AND (CI_prev > 0.6)
All signals are evaluated on bar close. The crossover and crossunder functions ensure signals fire only once when conditions transition from false to true.
Phase 7: Field Strength and Visualization Metrics
Average Amplitude :
avg_amp = (Σ osc_amps ) / N
Field Strength :
field_strength = CI × avg_amp
Collapse Risk (for dashboard):
collapse_risk = (CI - CI) / max(CI , 0.1)
collapse_risk_pct = clamp(collapse_risk × 100, 0, 100)
Quantum State Classification :
if (CI > threshold AND phase_locked):
state = "Ignition"
else if (CI > 0.6):
state = "Coherent"
else if (collapse):
state = "Collapse"
else:
state = "Chaos"
Phase 8: Visual Rendering
Orbit Plot : For each oscillator, convert polar (phase, amplitude) to Cartesian (x, y) for grid placement:
radius = amplitude × grid_center × 0.8
x = radius × cos(phase × π/180)
y = radius × sin(phase × π/180)
col = center + x (mapped to grid coordinates)
row = center - y
Heat Map : For each oscillator row and time column, retrieve historical phase value at lookback = (columns - col) × sample_rate, then map phase to color using a hue gradient.
Entanglement Web : Render matrix as table cell with background color opacity = E(i,j).
Field Cloud : Background color = (phi_dom > -90 AND phi_dom < 90) ? green : red, with opacity = mix(min_opacity, max_opacity, CI).
All visual components render only on the last bar (barstate.islast) to minimize computational overhead.
How to Use This Indicator
Step 1 : Apply QRFM to your chart. It works on all timeframes and asset classes, though 15-minute to 4-hour timeframes provide the best balance of responsiveness and noise reduction.
Step 2 : Enable the dashboard (default: top right) and the circular orbit plot (default: middle left). These are your primary visual feedback tools.
Step 3 : Optionally enable the heat map, entanglement web, and field cloud based on your preference. New users may find all visuals overwhelming; start with dashboard + orbit plot.
Step 4 : Observe for 50-100 bars to let the indicator establish baseline coherence patterns. Markets have different "normal" CI ranges—some instruments naturally run higher or lower coherence.
Understanding the Circular Orbit Plot
The orbit plot is a polar grid showing oscillator vectors in real-time:
Center point : Neutral (zero phase and amplitude)
Each vector : A line from center to a point on the grid
Vector angle : The oscillator's phase (0° = right/east, 90° = up/north, 180° = left/west, -90° = down/south)
Vector length : The oscillator's amplitude (short = weak signal, long = strong signal)
Vector label : First letter of oscillator name (R = RSI, M = MACD, etc.)
What to watch :
Convergence : When all vectors cluster in one quadrant or sector, CI is rising and coherence is forming. This is your pre-signal warning.
Scatter : When vectors point in random directions (360° spread), CI is low and the market is in a non-trending or transitional regime.
Rotation : When the cluster rotates smoothly around the circle, the ensemble is in coherent oscillation—typically seen during steady trends.
Sudden flips : When the cluster rapidly jumps from one side to the opposite (e.g., +90° to -90°), a phase reversal has occurred—often coinciding with trend reversals.
Example: If you see RSI, MACD, and Stochastic all pointing toward 45° (northeast) with long vectors, while CCI, TSI, and ROC point toward 40-50° as well, coherence is high and dominant phase is bullish. Expect an ignition signal if CI crosses threshold.
Reading Dashboard Metrics
The dashboard provides numerical confirmation of what the orbit plot shows visually:
CI : Displays as 0-100%. Above 70% = high coherence (strong regime), 40-70% = moderate, below 40% = low (poor conditions for trend entries).
Dom Phase : Angle in degrees with directional arrow. ⬆ = bullish bias, ⬇ = bearish bias, ⬌ = neutral.
Field Strength : CI weighted by amplitude. High values (> 0.6) indicate not just alignment but strong alignment.
Entangled Pairs : Count of oscillator pairs with E > threshold. Higher = more confirmation. If minimum is set to 4, you need at least 4 pairs entangled for signals.
Phase Lock : 🔒 YES (all oscillators within tolerance) or 🔓 NO (spread too wide).
State : Real-time classification:
🚀 IGNITION: CI just crossed threshold with phase-lock
⚡ COHERENT: CI is high and stable
💥 COLLAPSE: CI has dropped sharply
🌀 CHAOS: Low CI, scattered phases
Collapse Risk : 0-100% scale based on recent CI change. Above 50% warns of imminent breakdown.
Interpreting Signals
Long Ignition (Blue Triangle Below Price) :
Occurs when CI crosses above threshold (e.g., 0.80)
Dominant phase is in bullish range (-90° to +90°)
All oscillators are phase-locked (within tolerance)
Minimum entangled pairs requirement met
Interpretation : The oscillator ensemble has transitioned from disorder to coherent bullish alignment. This is a high-probability long entry point. The multi-layer confirmation (CI + phase direction + lock + entanglement) ensures this is not a single-oscillator whipsaw.
Short Ignition (Red Triangle Above Price) :
Same conditions as long, but dominant phase is in bearish range (< -90° or > +90°)
Interpretation : Coherent bearish alignment has formed. High-probability short entry.
Collapse (Circles Above and Below Price) :
CI has dropped by more than the collapse threshold (e.g., 0.55) over a 5-bar window
CI was previously above 0.6 (collapsing from coherent state)
Interpretation : Phase coherence has broken down. If you are in a position, this is an exit warning. If looking to enter, stand aside—regime is transitioning.
Phase-Time Heat Map Patterns
Enable the heat map and position it at bottom right. The rows represent individual oscillators, columns represent time bins (most recent on left).
Pattern: Horizontal Color Bands
If a row (e.g., RSI) shows consistent color across columns (say, green for several bins), that oscillator has maintained stable phase over time. If all rows show horizontal bands of similar color, the entire ensemble has been phase-locked for an extended period—this is a strong trending regime.
Pattern: Vertical Color Bands
If a column (single time bin) shows all cells with the same or very similar color, that moment in time had high coherence. These vertical bands often align with ignition signals or major price pivots.
Pattern: Rainbow Chaos
If cells are random colors (red, green, yellow mixed with no pattern), coherence is low. The ensemble is scattered. Avoid trading during these periods unless you have external confirmation.
Pattern: Color Transition
If you see a row transition from red to green (or vice versa) sharply, that oscillator has phase-flipped. If multiple rows do this simultaneously, a regime change is underway.
Entanglement Web Analysis
Enable the web matrix (default: opposite corner from heat map). It shows an N×N grid where N = number of active oscillators.
Bright Yellow/Gold Cells : High pairwise entanglement. For example, if the RSI-MACD cell is bright gold, those two oscillators are moving in phase. If the RSI-Stochastic cell is bright, they are entangled as well.
Dark Gray Cells : Low entanglement. Oscillators are decorrelated or in quadrature.
Diagonal : Always marked with "—" because an oscillator is always perfectly entangled with itself.
How to use :
Scan for clustering: If most cells are bright, coherence is high across the board. If only a few cells are bright, coherence is driven by a subset (e.g., RSI and MACD are aligned, but nothing else is—weak signal).
Identify laggards: If one row/column is entirely dark, that oscillator is the outlier. You may choose to disable it or monitor for when it joins the group (late confirmation).
Watch for web formation: During low-coherence periods, the matrix is mostly dark. As coherence builds, cells begin lighting up. A sudden "web" of connections forming visually precedes ignition signals.
Trading Workflow
Step 1: Monitor Coherence Level
Check the dashboard CI metric or observe the orbit plot. If CI is below 40% and vectors are scattered, conditions are poor for trend entries. Wait.
Step 2: Detect Coherence Building
When CI begins rising (say, from 30% to 50-60%) and you notice vectors on the orbit plot starting to cluster, coherence is forming. This is your alert phase—do not enter yet, but prepare.
Step 3: Confirm Phase Direction
Check the dominant phase angle and the orbit plot quadrant where clustering is occurring:
Clustering in right half (0° to ±90°): Bullish bias forming
Clustering in left half (±90° to 180°): Bearish bias forming
Verify the dashboard shows the corresponding directional arrow (⬆ or ⬇).
Step 4: Wait for Signal Confirmation
Do not enter based on rising CI alone. Wait for the full ignition signal:
CI crosses above threshold
Phase-lock indicator shows 🔒 YES
Entangled pairs count >= minimum
Directional triangle appears on chart
This ensures all layers have aligned.
Step 5: Execute Entry
Long : Blue triangle below price appears → enter long
Short : Red triangle above price appears → enter short
Step 6: Position Management
Initial Stop : Place stop loss based on your risk management rules (e.g., recent swing low/high, ATR-based buffer).
Monitoring :
Watch the field cloud density. If it remains opaque and colored in your direction, the regime is intact.
Check dashboard collapse risk. If it rises above 50%, prepare for exit.
Monitor the orbit plot. If vectors begin scattering or the cluster flips to the opposite side, coherence is breaking.
Exit Triggers :
Collapse signal fires (circles appear)
Dominant phase flips to opposite half-plane
CI drops below 40% (coherence lost)
Price hits your profit target or trailing stop
Step 7: Post-Exit Analysis
After exiting, observe whether a new ignition forms in the opposite direction (reversal) or if CI remains low (transition to range). Use this to decide whether to re-enter, reverse, or stand aside.
Best Practices
Use Price Structure as Context
QRFM identifies when coherence forms but does not specify where price will go. Combine ignition signals with support/resistance levels, trendlines, or chart patterns. For example:
Long ignition near a major support level after a pullback: high-probability bounce
Long ignition in the middle of a range with no structure: lower probability
Multi-Timeframe Confirmation
Open QRFM on two timeframes simultaneously:
Higher timeframe (e.g., 4-hour): Use CI level to determine regime bias. If 4H CI is above 60% and dominant phase is bullish, the market is in a bullish regime.
Lower timeframe (e.g., 15-minute): Execute entries on ignition signals that align with the higher timeframe bias.
This prevents counter-trend trades and increases win rate.
Distinguish Between Regime Types
High CI, stable dominant phase (State: Coherent) : Trending market. Ignitions are continuation signals; collapses are profit-taking or reversal warnings.
Low CI, erratic dominant phase (State: Chaos) : Ranging or choppy market. Avoid ignition signals or reduce position size. Wait for coherence to establish.
Moderate CI with frequent collapses : Whipsaw environment. Use wider stops or stand aside.
Adjust Parameters to Instrument and Timeframe
Crypto/Forex (high volatility) : Lower ignition threshold (0.65-0.75), lower CI smoothing (2-3), shorter oscillator lengths (7-10).
Stocks/Indices (moderate volatility) : Standard settings (threshold 0.75-0.85, smoothing 5-7, oscillator lengths 14).
Lower timeframes (5-15 min) : Reduce phase sample rate to 1-2 for responsiveness.
Higher timeframes (daily+) : Increase CI smoothing and oscillator lengths for noise reduction.
Use Entanglement Count as Conviction Filter
The minimum entangled pairs setting controls signal strictness:
Low (1-2) : More signals, lower quality (acceptable if you have other confirmation)
Medium (3-5) : Balanced (recommended for most traders)
High (6+) : Very strict, fewer signals, highest quality
Adjust based on your trade frequency preference and risk tolerance.
Monitor Oscillator Contribution
Use the entanglement web to see which oscillators are driving coherence. If certain oscillators are consistently dark (low E with all others), they may be adding noise. Consider disabling them. For example:
On low-volume instruments, MFI may be unreliable → disable MFI
On strongly trending instruments, mean-reversion oscillators (Stochastic, RSI) may lag → reduce weight or disable
Respect the Collapse Signal
Collapse events are early warnings. Price may continue in the original direction for several bars after collapse fires, but the underlying regime has weakened. Best practice:
If in profit: Take partial or full profit on collapse
If at breakeven/small loss: Exit immediately
If collapse occurs shortly after entry: Likely a false ignition; exit to avoid drawdown
Collapses do not guarantee immediate reversals—they signal uncertainty .
Combine with Volume Analysis
If your instrument has reliable volume:
Ignitions with expanding volume: Higher conviction
Ignitions with declining volume: Weaker, possibly false
Collapses with volume spikes: Strong reversal signal
Collapses with low volume: May just be consolidation
Volume is not built into QRFM (except via MFI), so add it as external confirmation.
Observe the Phase Spiral
The spiral provides a quick visual cue for rotation consistency:
Tight, smooth spiral : Ensemble is rotating coherently (trending)
Loose, erratic spiral : Phase is jumping around (ranging or transitional)
If the spiral tightens, coherence is building. If it loosens, coherence is dissolving.
Do Not Overtrade Low-Coherence Periods
When CI is persistently below 40% and the state is "Chaos," the market is not in a regime where phase analysis is predictive. During these times:
Reduce position size
Widen stops
Wait for coherence to return
QRFM's strength is regime detection. If there is no regime, the tool correctly signals "stand aside."
Use Alerts Strategically
Set alerts for:
Long Ignition
Short Ignition
Collapse
Phase Lock (optional)
Configure alerts to "Once per bar close" to avoid intrabar repainting and noise. When an alert fires, manually verify:
Orbit plot shows clustering
Dashboard confirms all conditions
Price structure supports the trade
Do not blindly trade alerts—use them as prompts for analysis.
Ideal Market Conditions
Best Performance
Instruments :
Liquid, actively traded markets (major forex pairs, large-cap stocks, major indices, top-tier crypto)
Instruments with clear cyclical oscillator behavior (avoid extremely illiquid or manipulated markets)
Timeframes :
15-minute to 4-hour: Optimal balance of noise reduction and responsiveness
1-hour to daily: Slower, higher-conviction signals; good for swing trading
5-minute: Acceptable for scalping if parameters are tightened and you accept more noise
Market Regimes :
Trending markets with periodic retracements (where oscillators cycle through phases predictably)
Breakout environments (coherence forms before/during breakout; collapse occurs at exhaustion)
Rotational markets with clear swings (oscillators phase-lock at turning points)
Volatility :
Moderate to high volatility (oscillators have room to move through their ranges)
Stable volatility regimes (sudden VIX spikes or flash crashes may create false collapses)
Challenging Conditions
Instruments :
Very low liquidity markets (erratic price action creates unstable oscillator phases)
Heavily news-driven instruments (fundamentals may override technical coherence)
Highly correlated instruments (oscillators may all reflect the same underlying factor, reducing independence)
Market Regimes :
Deep, prolonged consolidation (oscillators remain near neutral, CI is chronically low, few signals fire)
Extreme chop with no directional bias (oscillators whipsaw, coherence never establishes)
Gap-driven markets (large overnight gaps create phase discontinuities)
Timeframes :
Sub-5-minute charts: Noise dominates; oscillators flip rapidly; coherence is fleeting and unreliable
Weekly/monthly: Oscillators move extremely slowly; signals are rare; better suited for long-term positioning than active trading
Special Cases :
During major economic releases or earnings: Oscillators may lag price or become decorrelated as fundamentals overwhelm technicals. Reduce position size or stand aside.
In extremely low-volatility environments (e.g., holiday periods): Oscillators compress to neutral, CI may be artificially high due to lack of movement, but signals lack follow-through.
Adaptive Behavior
QRFM is designed to self-adapt to poor conditions:
When coherence is genuinely absent, CI remains low and signals do not fire
When only a subset of oscillators aligns, entangled pairs count stays below threshold and signals are filtered out
When phase-lock cannot be achieved (oscillators too scattered), the lock filter prevents signals
This means the indicator will naturally produce fewer (or zero) signals during unfavorable conditions, rather than generating false signals. This is a feature —it keeps you out of low-probability trades.
Parameter Optimization by Trading Style
Scalping (5-15 Minute Charts)
Goal : Maximum responsiveness, accept higher noise
Oscillator Lengths :
RSI: 7-10
MACD: 8/17/6
Stochastic: 8-10, smooth 2-3
CCI: 14-16
Others: 8-12
Coherence Settings :
CI Smoothing Window: 2-3 bars (fast reaction)
Phase Sample Rate: 1 (every bar)
Ignition Threshold: 0.65-0.75 (lower for more signals)
Collapse Threshold: 0.40-0.50 (earlier exit warnings)
Confirmation :
Phase Lock Tolerance: 40-50° (looser, easier to achieve)
Min Entangled Pairs: 2-3 (fewer oscillators required)
Visuals :
Orbit Plot + Dashboard only (reduce screen clutter for fast decisions)
Disable heavy visuals (heat map, web) for performance
Alerts :
Enable all ignition and collapse alerts
Set to "Once per bar close"
Day Trading (15-Minute to 1-Hour Charts)
Goal : Balance between responsiveness and reliability
Oscillator Lengths :
RSI: 14 (standard)
MACD: 12/26/9 (standard)
Stochastic: 14, smooth 3
CCI: 20
Others: 10-14
Coherence Settings :
CI Smoothing Window: 3-5 bars (balanced)
Phase Sample Rate: 2-3
Ignition Threshold: 0.75-0.85 (moderate selectivity)
Collapse Threshold: 0.50-0.55 (balanced exit timing)
Confirmation :
Phase Lock Tolerance: 30-40° (moderate tightness)
Min Entangled Pairs: 4-5 (reasonable confirmation)
Visuals :
Orbit Plot + Dashboard + Heat Map or Web (choose one)
Field Cloud for regime backdrop
Alerts :
Ignition and collapse alerts
Optional phase-lock alert for advance warning
Swing Trading (4-Hour to Daily Charts)
Goal : High-conviction signals, minimal noise, fewer trades
Oscillator Lengths :
RSI: 14-21
MACD: 12/26/9 or 19/39/9 (longer variant)
Stochastic: 14-21, smooth 3-5
CCI: 20-30
Others: 14-20
Coherence Settings :
CI Smoothing Window: 5-10 bars (very smooth)
Phase Sample Rate: 3-5
Ignition Threshold: 0.80-0.90 (high bar for entry)
Collapse Threshold: 0.55-0.65 (only significant breakdowns)
Confirmation :
Phase Lock Tolerance: 20-30° (tight clustering required)
Min Entangled Pairs: 5-7 (strong confirmation)
Visuals :
All modules enabled (you have time to analyze)
Heat Map for multi-bar pattern recognition
Web for deep confirmation analysis
Alerts :
Ignition and collapse
Review manually before entering (no rush)
Position/Long-Term Trading (Daily to Weekly Charts)
Goal : Rare, very high-conviction regime shifts
Oscillator Lengths :
RSI: 21-30
MACD: 19/39/9 or 26/52/12
Stochastic: 21, smooth 5
CCI: 30-50
Others: 20-30
Coherence Settings :
CI Smoothing Window: 10-14 bars
Phase Sample Rate: 5 (every 5th bar to reduce computation)
Ignition Threshold: 0.85-0.95 (only extreme alignment)
Collapse Threshold: 0.60-0.70 (major regime breaks only)
Confirmation :
Phase Lock Tolerance: 15-25° (very tight)
Min Entangled Pairs: 6+ (broad consensus required)
Visuals :
Dashboard + Orbit Plot for quick checks
Heat Map to study historical coherence patterns
Web to verify deep entanglement
Alerts :
Ignition only (collapses are less critical on long timeframes)
Manual review with fundamental analysis overlay
Performance Optimization (Low-End Systems)
If you experience lag or slow rendering:
Reduce Visual Load :
Orbit Grid Size: 8-10 (instead of 12+)
Heat Map Time Bins: 5-8 (instead of 10+)
Disable Web Matrix entirely if not needed
Disable Field Cloud and Phase Spiral
Reduce Calculation Frequency :
Phase Sample Rate: 5-10 (calculate every 5-10 bars)
Max History Depth: 100-200 (instead of 500+)
Disable Unused Oscillators :
If you only want RSI, MACD, and Stochastic, disable the other five. Fewer oscillators = smaller matrices, faster loops.
Simplify Dashboard :
Choose "Small" dashboard size
Reduce number of metrics displayed
These settings will not significantly degrade signal quality (signals are based on bar-close calculations, which remain accurate), but will improve chart responsiveness.
Important Disclaimers
This indicator is a technical analysis tool designed to identify periods of phase coherence across an ensemble of oscillators. It is not a standalone trading system and does not guarantee profitable trades. The Coherence Index, dominant phase, and entanglement metrics are mathematical calculations applied to historical price data—they measure past oscillator behavior and do not predict future price movements with certainty.
No Predictive Guarantee : High coherence indicates that oscillators are currently aligned, which historically has coincided with trending or directional price movement. However, past alignment does not guarantee future trends. Markets can remain coherent while prices consolidate, or lose coherence suddenly due to news, liquidity changes, or other factors not captured by oscillator mathematics.
Signal Confirmation is Probabilistic : The multi-layer confirmation system (CI threshold + dominant phase + phase-lock + entanglement) is designed to filter out low-probability setups. This increases the proportion of valid signals relative to false signals, but does not eliminate false signals entirely. Users should combine QRFM with additional analysis—support and resistance levels, volume confirmation, multi-timeframe alignment, and fundamental context—before executing trades.
Collapse Signals are Warnings, Not Reversals : A coherence collapse indicates that the oscillator ensemble has lost alignment. This often precedes trend exhaustion or reversals, but can also occur during healthy pullbacks or consolidations. Price may continue in the original direction after a collapse. Use collapses as risk management cues (tighten stops, take partial profits) rather than automatic reversal entries.
Market Regime Dependency : QRFM performs best in markets where oscillators exhibit cyclical, mean-reverting behavior and where trends are punctuated by retracements. In markets dominated by fundamental shocks, gap openings, or extreme low-liquidity conditions, oscillator coherence may be less reliable. During such periods, reduce position size or stand aside.
Risk Management is Essential : All trading involves risk of loss. Use appropriate stop losses, position sizing, and risk-per-trade limits. The indicator does not specify stop loss or take profit levels—these must be determined by the user based on their risk tolerance and account size. Never risk more than you can afford to lose.
Parameter Sensitivity : The indicator's behavior changes with input parameters. Aggressive settings (low thresholds, loose tolerances) produce more signals with lower average quality. Conservative settings (high thresholds, tight tolerances) produce fewer signals with higher average quality. Users should backtest and forward-test parameter sets on their specific instruments and timeframes before committing real capital.
No Repainting by Design : All signal conditions are evaluated on bar close using bar-close values. However, the visual components (orbit plot, heat map, dashboard) update in real-time during bar formation for monitoring purposes. For trade execution, rely on the confirmed signals (triangles and circles) that appear only after the bar closes.
Computational Load : QRFM performs extensive calculations, including nested loops for entanglement matrices and real-time table rendering. On lower-powered devices or when running multiple indicators simultaneously, users may experience lag. Use the performance optimization settings (reduce visual complexity, increase phase sample rate, disable unused oscillators) to improve responsiveness.
This system is most effective when used as one component within a broader trading methodology that includes sound risk management, multi-timeframe analysis, market context awareness, and disciplined execution. It is a tool for regime detection and signal confirmation, not a substitute for comprehensive trade planning.
Technical Notes
Calculation Timing : All signal logic (ignition, collapse) is evaluated using bar-close values. The barstate.isconfirmed or implicit bar-close behavior ensures signals do not repaint. Visual components (tables, plots) render on every tick for real-time feedback but do not affect signal generation.
Phase Wrapping : Phase angles are calculated in the range -180° to +180° using atan2. Angular distance calculations account for wrapping (e.g., the distance between +170° and -170° is 20°, not 340°). This ensures phase-lock detection works correctly across the ±180° boundary.
Array Management : The indicator uses fixed-size arrays for oscillator phases, amplitudes, and the entanglement matrix. The maximum number of oscillators is 8. If fewer oscillators are enabled, array sizes shrink accordingly (only active oscillators are processed).
Matrix Indexing : The entanglement matrix is stored as a flat array with size N×N, where N is the number of active oscillators. Index mapping: index(row, col) = row × N + col. Symmetric pairs (i,j) and (j,i) are stored identically.
Normalization Stability : Oscillators are normalized to using fixed reference levels (e.g., RSI overbought/oversold at 70/30). For unbounded oscillators (MACD, ROC, TSI), statistical normalization (division by rolling standard deviation) is used, with clamping to prevent extreme outliers from distorting phase calculations.
Smoothing and Lag : The CI smoothing window (SMA) introduces lag proportional to the window size. This is intentional—it filters out single-bar noise spikes in coherence. Users requiring faster reaction can reduce the smoothing window to 1-2 bars, at the cost of increased sensitivity to noise.
Complex Number Representation : Pine Script does not have native complex number types. Complex arithmetic is implemented using separate real and imaginary accumulators (sum_cos, sum_sin) and manual calculation of magnitude (sqrt(real² + imag²)) and argument (atan2(imag, real)).
Lookback Limits : The indicator respects Pine Script's maximum lookback constraints. Historical phase and amplitude values are accessed using the operator, with lookback limited to the chart's available bar history (max_bars_back=5000 declared).
Visual Rendering Performance : Tables (orbit plot, heat map, web, dashboard) are conditionally deleted and recreated on each update using table.delete() and table.new(). This prevents memory leaks but incurs redraw overhead. Rendering is restricted to barstate.islast (last bar) to minimize computational load—historical bars do not render visuals.
Alert Condition Triggers : alertcondition() functions evaluate on bar close when their boolean conditions transition from false to true. Alerts do not fire repeatedly while a condition remains true (e.g., CI stays above threshold for 10 bars fires only once on the initial cross).
Color Gradient Functions : The phaseColor() function maps phase angles to RGB hues using sine waves offset by 120° (red, green, blue channels). This creates a continuous spectrum where -180° to +180° spans the full color wheel. The amplitudeColor() function maps amplitude to grayscale intensity. The coherenceColor() function uses cos(phase) to map contribution to CI (positive = green, negative = red).
No External Data Requests : QRFM operates entirely on the chart's symbol and timeframe. It does not use request.security() or access external data sources. All calculations are self-contained, avoiding lookahead bias from higher-timeframe requests.
Deterministic Behavior : Given identical input parameters and price data, QRFM produces identical outputs. There are no random elements, probabilistic sampling, or time-of-day dependencies.
— Dskyz, Engineering precision. Trading coherence.
ค้นหาในสคริปต์สำหรับ "Exponential"
IIR One-Pole Price Filter [BackQuant]IIR One-Pole Price Filter
A lightweight, mathematically grounded smoothing filter derived from signal processing theory, designed to denoise price data while maintaining minimal lag. It provides a refined alternative to the classic Exponential Moving Average (EMA) by directly controlling the filter’s responsiveness through three interchangeable alpha modes: EMA-Length , Half-Life , and Cutoff-Period .
Concept overview
An IIR (Infinite Impulse Response) filter is a type of recursive filter that blends current and past input values to produce a smooth, continuous output. The "one-pole" version is its simplest form, consisting of a single recursive feedback loop that exponentially decays older price information. This makes it both memory-efficient and responsive , ideal for traders seeking a precise balance between noise reduction and reaction speed.
Unlike standard moving averages, the IIR filter can be tuned in physically meaningful terms (such as half-life or cutoff frequency) rather than just arbitrary periods. This allows the trader to think about responsiveness in the same way an engineer or physicist would interpret signal smoothing.
Why use it
Filters out market noise without introducing heavy lag like higher-order smoothers.
Adapts to various trading speeds and time horizons by changing how alpha (responsiveness) is parameterized.
Provides consistent and mathematically interpretable control of smoothing, suitable for both discretionary and algorithmic systems.
Can serve as the core component in adaptive strategies, volatility normalization, or trend extraction pipelines.
Alpha Modes Explained
EMA-Length : Classic exponential decay with alpha = 2 / (L + 1). Equivalent to a standard EMA but exposed directly for fine control.
Half-Life : Defines the number of bars it takes for the influence of a price input to decay by half. More intuitive for time-domain analysis.
Cutoff-Period : Inspired by analog filter theory, defines the cutoff frequency (in bars) beyond which price oscillations are heavily attenuated. Lower periods = faster response.
Formula in plain terms
Each bar updates as:
yₜ = yₜ₋₁ + alpha × (priceₜ − yₜ₋₁)
Where alpha is the smoothing coefficient derived from your chosen mode.
Smaller alpha → smoother but slower response.
Larger alpha → faster but noisier response.
Practical application
Trend detection : When the filter line rises, momentum is positive; when it falls, momentum is negative.
Signal timing : Use the crossover of the filter vs its previous value (or price) as an entry/exit condition.
Noise suppression : Apply on volatile assets or lower timeframes to remove flicker from raw price data.
Foundation for advanced filters : The one-pole IIR serves as a building block for multi-pole cascades, adaptive smoothers, and spectral filters.
Customization options
Alpha Scale : Multiplies the final alpha to fine-tune aggressiveness without changing the mode’s core math.
Color Painting : Candles can be painted green/red by trend direction for visual clarity.
Line Width & Transparency : Adjust the visual intensity to integrate cleanly with your charting style.
Interpretation tips
A smooth yet reactive line implies optimal tuning — minimal delay with reduced false flips.
A sluggish line suggests alpha is too small (increase responsiveness).
A noisy, twitchy line means alpha is too large (increase smoothing).
Half-life tuning often feels more natural for aligning filter speed with price cycles or bar duration.
Summary
The IIR One-Pole Price Filter is a signal smoother that merges simplicity with mathematical rigor. Whether you’re filtering for entry signals, generating trend overlays, or constructing larger multi-stage systems, this filter delivers stability, clarity, and precision control over noise versus lag, an essential tool for any quantitative or systematic trading approach.
EWMA & EWVar + EWStd Expansion with MTF_V.5EWMA & EWVar + EWStd Expansion with MTF_V.5
This indicator combines adaptive trend smoothing (EWMA), variance estimation (EWVar) and dynamic volatility “bursts” (EWStd Expansion) with optional higher-timeframe confirmation. It’s designed both for visual chart analysis and for automated alerts on regime changes.
Key Features
EWMA (Exponential Smoothing):
• Computes an exponential moving average with either a custom α or a length-derived α = 2/(N+1).
• Option to recalculate only every N bars (reduces CPU load).
EWVar & EWStd (Variance & Standard Deviation):
• Exponentially weighted variance tracks recent price dispersion.
• EWStd (σ) is computed alongside the EWMA.
• Z-score (deviation in σ units) shows how far price has diverged from trend.
Multi-Timeframe Filter (MTF):
• Optionally require the same trend direction on a chosen higher timeframe (e.g. Daily, Weekly, H4).
• Real-time lookahead available (may repaint).
Gradient Around EWMA:
• A multi-layer “glow” zone of ±1σ, broken into up to 10 steps.
• Color interpolates between “upper” and “lower” shades for bullish, bearish and neutral regimes.
Instantaneous Trendline (ITL):
• Ultra-fast trend filter with slope-based coloring.
• Highlights micro-trends and short-lived accelerations.
Cross-Over Signals (ITL ↔ EWMA):
• Up/down triangles plotted when the ITL crosses the main EWMA.
EWStd Expansion (Volatility Bursts):
• Automatically detects σ expansions (σ growth above a set % threshold).
• Price filter: only when price moves beyond EWMA ± (multiplier·σ).
• Optional higher-timeframe confirmation.
Labels & Alerts:
• Text labels and circular markers on bars where a volatility burst occurs.
• Built-in alertcondition calls for both bullish and bearish expansions.
How to Use
Visual Analysis:
• The gradient around EWMA shows the width of the volatility channel expanding or contracting.
• ITL color changes instantly highlight short-term impulses.
• EWMA line color switches (bullish/bearish/neutral) indicate trend state.
Spotting Volatility Breakouts:
• “EWStd Expansion” labels and circles signal the onset of strong moves when σ spikes.
• Useful for entering at the start of new impulses.
Automated Alerts:
• Set alerts on the built-in conditions “Bullish EWStd Expansion Alert” or “Bearish EWStd Expansion Alert” to receive a popup or mobile push when a burst occurs.
This compact tool unifies trend, volatility and multi-timeframe analysis into a single indicator—ideal for traders who want to see trend direction, current dispersion, and timely volatility burst signals all at once.
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
6 Dynamic EMAs by Koenigsegg🚀 6 Dynamic EMAs by Koenigsegg
Take control of your chart with ultimate flexibility. This tool gives you 6 customizable EMAs across any timeframe, helping you read the market like a pro — whether you're scalping seconds or swinging days. Built for precision, designed for dominance.
The combinations? Endless. Mix and match any EMA lengths and timeframes for tailored confluence — exactly how elite traders operate.
🔑 Key Features
✅ 6 Fully Customizable EMAs
⏳ Multi-Timeframe Support (from seconds to months)
🎨 Custom Colors & Thickness for each EMA
🚨 Built-in Cross Alerts for instant trade signals
🧠 Clean, efficient logic using request.security()
🔁 Dynamically toggle EMAs on/off
⚙️ Lightweight for smooth chart performance
🧩 Endless combo potential — confluence on your terms
📈 What Is an EMA?
The EMA is a type of moving average that adjusts more quickly to recent price changes than a Simple Moving Average (SMA). It does this by giving exponentially more weight to the most recent candles.
⚙️ How Does It Function?
Smoothing Price Data:
It takes the average of closing prices over a chosen period (like 20 or 50 candles), but gives more influence to the latest prices.
Reacts Quickly to Price Shifts:
Since recent data is weighted more heavily, the EMA adjusts faster to sudden price changes — helping you spot trend reversals or momentum shifts earlier.
Dynamic Support & Resistance:
Traders often use EMAs as moving support/resistance levels. Price often "respects" EMAs in trending markets — bouncing off them during pullbacks.
Trend Confirmation:
- If price is above the EMA, the market is likely in an uptrend.
- If price is below the EMA, the market is likely in a downtrend.
- Multiple EMAs (like 12/21 or 50/200) crossing each other are used for entry/exit signals.
💡 Example:
If you use a 21 EMA on a chart, it shows you the average price of the last 21 candles, but the most recent ones weigh heavier. This makes the EMA more responsive than an SMA, and better for short-term or active trading.
📊 Why EMAs Matter — and How Multi-Timeframe EMAs Give You the Edge
Exponential Moving Averages (EMAs) are essential tools for identifying trend direction, momentum shifts, and dynamic support/resistance. Because they weight recent price data more heavily, EMAs adapt quickly to changing market conditions, giving traders early insight into reversals or continuations.
Where this script shines is in its multi-timeframe (MTF) capability. For example, plotting a daily EMA on a 4H chart gives you high-level directional guidance while still allowing precision entries. This enables confluence between LTF (low timeframe) signals and HTF (high timeframe) momentum — a crucial edge used by institutional-level traders.
You can configure the tool to run classic combos like the 12/21 crossover on your current chart, while layering in a 50 or 200 EMA from a higher timeframe for macro confirmation. The 6th EMA, colored light blue by default, is perfect for adding one final level of structure insight — often used as a long-term anchor or trend bias marker.
Whether you're riding the wave or catching the reversal, these EMAs serve as your adaptable compass in every environment.
🎯 Purpose
This indicator was built to give traders a clear, responsive, and multi-timeframe edge using dynamic Exponential Moving Averages. Whether you're trend-following, identifying momentum shifts, or building a confluence system — these 6 EMAs are here to align with your strategy and style.
💡 Pro Tip
Instead of cluttering your chart with multiple EMA indicators, this script consolidates all into one sleek tool. You can toggle off bands you don't currently need, like running only the 12/21 EMAs on your active chart timeframe, while adding the 12/21 EMAs from a higher timeframe to guide trade decisions.
With this setup, you're not just reacting — you're orchestrating your trades with intention.
⚠️ Disclaimer
This script is for educational and informational purposes only. It does not constitute financial advice. Always do your own research and trade responsibly. Past performance does not guarantee future results.
Squeeze Index [LuxAlgo]The Squeeze Index aims to measure the action of price being squeezed, and is expressed as a percentage, with higher values suggesting prices are subject to a higher degree of compression.
Settings
Convergence Factor: Convergence factor of exponential envelopes.
Length: Period of the indicator.
Src: Source input of the indicator.
Usage
Prices being squeezed refer to the action of price being compressed within a tightening area. Prices in a tight area logically indicate a period of stationarity, price breaking out of this area will generally indicate the trader whether to buy or sell depending on the breakout direction.
The convergence factor and length settings both play an important role in the returned indicator values. A convergence factor greater than the period value will detect more squeezed prices area, while a period greater than the convergence will return fewer detected squeezed areas.
We recommend using a convergence factor equal to the period setting or a convergence factor twice as high.
The above chart makes use of a convergence factor of 100 and a period of 10.
Due to the calculation method, it is possible to see retracements being interpreted as price squeezing. This effect can be emphasized with higher convergence factor values.
Details
In order to measure the effect of price being squeezed in a tighter area we refer to damping, where the oscillations amplitude of a system decrease over time. If the envelopes of a damped system can be estimated, then getting the difference between the upper and lower extremity of these envelopes would return a decreasing series of values.
This approach is used here. First the difference between the exponential envelopes extremities is obtained, the logarithm of this difference if obtained due to the extremities converging exponentially toward their input.
We then use the correlation oscillator to get a scaled measurement.
Multi Level ZigZag Harmonic PatternsLets make things bit complicated.
Main difference between this script and the earlier Multi Zigzag Harmonic Pattern is the calculation logic of Zigzag 2, 3 and 4
In the earlier script, all zigzags were plain and were calculated on the basis of different lengths. (Such as 5, 10, 15, 20). These were derived on the basis of Multi Zigzag indicator
In this script, Zigzag 2, 3 and 4 are calculated in slightly different way. They are calculated on the basis of previous zigzag. This means, Zigzag 1 will be the input for Zigzag2 calculation and Zigzag 2 will be the input for Zigzag3 and so on. This is demonstrated in the script - Multi Level Zigzag
One important parameter which is specific to this script is: UseZigZagChain
If checked:
Zigzag2 is formed based on Zigzag1
Zigzag3 is formed based on Zigzag2
Zigzag4 is formed based on Zigzag3
This can lead to patterns covering huge number of candles as this chaining causes exponential effect in each levels. (Effective length grows exponentially in each level)
If unchecked:
Zigzag2 is formed based on Zigzag1 (Same as when checked)
Zigzag3 is formed based on Zigzag1. But, length is set to zigzag2Length + zigzag3Length
Zigzag4 is formed based on Zigzag1. But, length is set to zigzag2Length + zigzag3Length + zigzag4Length
This reduces exponential increase of zigzag lengths over next levels.
Logical ratios of patterns are coded as below:
Notations:
Lines XABCD forms the pattern in all cases. (OXABCD in case of Three drives )
abc = BC retacement of AB, xab = AB retracement of XA and so on
ABCD Classic
0.618 <= abc <= 0.786
1.272 <= bcd <= 1.618
AB=CD
Price difference between AB and CD are equal
Time difference between AB and CD are equal
ABCD Extension
0.618 <= abc <= 0.786
1.272 <= AD/ BC (price) <= 1.618
Gartley
xab = 0.618
0.382 <= abc <= 0.886
1.272 <= bcd <= 1.618 OR xad = 0.786
Crab
0.382 <= xab <= 0.618
0.382 <= abc <= 0.886
2.24 <= bcd <= 3.618 OR xad = 1.618
Deep Crab
xab = 0.886
0.382 <= abc <= 0.886
2.0 <= bcd <= 3.618 OR xad = 1.618
Bat
0.382 <= xab <= 0.50
0.382 <= abc <= 0.886
1.618 <= bcd <= 2.618 OR xad = 0.886
Butterfly
xab = 0.786
0.382 <= abc <= 0.886
1.618 <= bcd <= 2.618 OR 1.272 <= xad <= 2.618
Shark
xab = 0.786
1.13 <= abc <= 1.618
1.618 <= bcd <= 2.24 OR 0.886 <= xad <= 1.13
Cypher
0.382 <= xab <= 0.618
1.13 <= abc <= 1.414
1.272 <= bcd <= 2.0 OR xad = 0.786
Three Drives
oxa = 0.618
1.27 <= xab <= 1.618
abc = 0.618
1.27 <= bcd <= 1.618
5-0
1.13 <= xab <= 1.618
1.618 <= abc <= 2.24
bcd = 0.5
Double Bottom
Last two pivot High Lows make W shape
Last Pivot Low is higher than previous Last Pivot Low.
Last Pivot High is lower than previous last Pivot High.
Price has not gone below Last Pivot Low
Price breaks out of last Pivot High to complete W shape
Double Top
Last two pivot High Lows make M shape
Last Pivot Low is higher than previous Last Pivot Low.
Last Pivot High is lower than previous last Pivot High.
Price has not gone above Last Pivot High
Price breaks out of last Pivot Low to complete M shape
Acc/Dist. Cloud with Fractal Deviation Bands by @XeL_ArjonaACCUMULATION / DISTRIBUTION CLOUD with MORPHIC DEVIATION BANDS
Ver. 2.0.beta.23:08:2015
by Ricardo M. Arjona @XeL_Arjona
DISCLAIMER
The Following indicator/code IS NOT intended to be a formal investment advice or recommendation by the author, nor should be construed as such. Users will be fully responsible by their use regarding their own trading vehicles/assets.
The embedded code and ideas within this work are FREELY AND PUBLICLY available on the Web for NON LUCRATIVE ACTIVITIES and must remain as is.
Pine Script code MOD's and adaptations by @XeL_Arjona with special mention in regard of:
Buy (Bull) and Sell (Bear) "Power Balance Algorithm by Vadim Gimelfarb published at Stocks & Commodities V. 21:10 (68-72).
Custom Weighting Coefficient for Exponential Moving Average (nEMA) adaptation work by @XeL_Arjona with contribution help from @RicardoSantos at TradingView @pinescript chat room.
Morphic Numbers (PHI & Plastic) Pine Script adaptation from it's algebraic generation formulas by @XeL_Arjona
Fractal Deviation Bands idea by @XeL_Arjona
CHANGE LOG:
ACCUMULATION / DISTRIBUTION CLOUD: I decided to change it's name from the Buy to Sell Pressure. The code is essentially the same as older versions and they are the center core (VORTEX?) of all derived New stuff which are:
MORPHIC NUMBERS: The "Golden Ratio" expressed by the result of the constant "PHI" and the newer and same in characteristics "Plastic Number" expressed as "PN". For more information about this regard take a look at: HERE!
CUSTOM(K) EXPONENTIAL MOVING AVERAGE: Some code has cleaned from last version to include as custom function the nEMA , which use an additional input (K) to customise the way the "exponentially" is weighted from the custom array. For the purpose of this indicator, I implement a volatility algorithm using the Average True Range of last 9 periods multiplied by the morphic number used in the fractal study. (Golden Ratio as default) The result is very similar in response to classic EMA but tend to accelerate or decelerate much more responsive with wider bars presented in trending average.
FRACTAL DEVIATION BANDS: The main idea is based on the so useful Standard Deviation process to create Bands in favor of a multiplier (As John Bollinger used in it's own bands) from a custom array, in which for this case is the "Volume Pressure Moving Average" as the main Vortex for the "Fractallitly", so then apply as many "Child bands" using the older one as the new calculation array using the same morphic constant as multiplier (Like Fibonacci but with other approach rather than %ratios). Results are AWSOME! Market tend to accelerate or decelerate their Trend in favor of a Fractal approach. This bands try to catch them, so please experiment and feedback me your own observations.
EXTERNAL TICKER FOR VOLUME DATA: I Added a way to input volume data for this kind of study from external tickers. This is just a quicky-hack given that currently TradingView is not adding Volume to their Indexes so; maybe this is temporary by now. It seems that this part of the code is conflicting with intraday timeframes, so You are advised.
This CODE is versioned as BETA FOR TESTING PROPOSES. By now TradingView Admins are changing lot's of things internally, so maybe this could conflict with correct rendering of this study with special tickers or timeframes. I will try to code by itself just the core parts of this study in order to use them at discretion in other areas. ALL NEW IDEAS OR MODIFICATIONS to these indicator(s) are Welcome in favor to deploy a better and more accurate readings. I will be very glad to be notified at Twitter or TradingView accounts at: @XeL_Arjona
TASC 2023.06 Stochastic Distance Oscillator█ OVERVIEW
This script implements the stochastic distance oscillator (SDO) , a momentum indicator introduced by Vitali Apirine in an article featured in TASC's June 2023 edition of Traders' Tips . The SDO is a variation of the classic stochastic oscillator and is designed to identify overbought and oversold levels, as well as detect bull and bear trend changes.
█ CONCEPTS
Unlike the classic stochastic oscillator, which compares an asset's price to its past price range, the SDO measures the size of the current distance relative to the maximum-minimum distance range over a set number of periods. The current distance is defined as the distance between the current price and the price n periods ago.
The readings of the SDO can be used to identify the following states of the asset price:
Uptrend state: the oscillator crosses over 50 from a non-uptrend state.
Downtrend state: the oscillator crosses under -50 from a non-downtrend state.
Overbought state: the oscillator is in an uptrend and crosses -50 for the first time.
Oversold state: the oscillator is in a downtrend and crosses 50 for the first time.
Trend continuity: the oscillator crosses 0 in the direction of the current trend.
The script indicates these five conditions using on-chart signals and background coloring.
█ CALCULATIONS
The SDO is calculated as follows:
1. Calculate the distance between the current price and the price n periods ago, as well as the maximum and minimum distances for the selected lookback period. The author recommends using one of two values of n , 14 or 40 bars.
2. Calculate the time series % D that represents the relation between the asset's current distance and its distance range over a loockback period:
% D = (Abs(current distance) − Abs(minimum distance)) / (Abs(maximum distance) − Abs(minimum distance)) * 100
3. Use the calculated % D to obtain the SDO:
If the closing price is above the close n periods ago, SDO = % D
If the closing price is below the close n periods ago, SDO = −% D
If the closing price equals the close n periods ago or the current distance equals the minimum distance, SDO = 0
4. Smooth the SDO using an exponential moving average (EMA). The author recommends using an EMA in the range from 3 to 6 .
Adjustable input parameters include the number of periods n , the lookback period for calculating % D , the smoothing EMA length, and the overbought/oversold threshold level.
Kaufman Adaptive Moving AverageKaufman Adaptive Moving Average script.
This indicator was originally developed by Perry J. Kaufman (`Smarter Trading: Improving Performance in Changing Markets`, 1995).
MACDeA different style of MACD indicator with different period values of WEIGHTED and EXPONENTIAL MOVING AVERAGES INSTEAD OF only EXPONENTIAL.
Default MOVING AVERAGES ARE
faster period: 8bars EMA
slower period: 13 bars EMA
signal period: 5 bars WMA
TURKISH EXPLANATION:
MACD indikatörünün sadece üssel yerine AĞIRLIKLI ve ÜSSEL hareketli ortalamalar kullanılarak daha erken sinyaller alabilmek için daha kısa periyotlarla yorumlanması
fikir @kenyaborsa on twitter
yazar: KIVANÇ @fr3762 on twitter
Quad Rotation StochasticQuad Rotation Stochastic
The Quad Rotation Stochastic is a powerful and unique momentum oscillator that combines four different stochastic setups into one tool, providing an incredibly detailed view of market conditions. This multi-timeframe stochastic approach helps traders better anticipate trend continuations, reversals, and momentum shifts with greater precision than traditional single stochastic indicators.
Why this indicator is useful:
Multi-layered Momentum Analysis: Instead of relying on one stochastic, this script tracks four independent stochastic readings, smoothing out noise and confirming stronger signals.
Advanced Divergence Detection: It automatically identifies bullish and bearish divergences for each stochastic, helping traders spot potential reversals early.
Background Color Alerts: When a configurable number (e.g., 3 or 4) of the stochastics agree in direction and position (overbought/oversold), the background colors green (bullish) or red (bearish) to give instant visual cues.
ABCD Pattern Recognition: The script recognizes "shield" patterns when Stochastic 4 remains stuck at extreme levels (above 90 or below 10) for a set time, warning of potential trend continuation setups.
Super Signal Alerts: If all four stochastics align in extreme conditions and slope in the same direction, the indicator plots a special "Super Signal," offering high-confidence entry opportunities.
Why this indicator is unique:
Quad Confirmation Logic: Combining four different stochastics makes this tool much less prone to false signals compared to using a single stochastic.
Customizable Divergence Coloring: Traders can choose to have divergence lines automatically match the stochastic color for clear visual association.
Adaptive ABCD Shields: Innovative use of bar counting while a stochastic remains extreme acts as a "shield," offering a unique way to filter out minor fake-outs.
Flexible Configuration: Each stochastic's sensitivity, divergence settings, and visual styling can be fully customized, allowing traders to adapt it to their own strategy and asset.
Example Usage: Trading Bitcoin with Quad Rotation Stochastic
When trading Bitcoin (BTCUSD), you might set the minimum count (minCount) to 3, meaning three out of four stochastics must be in agreement to trigger a background color.
If the background turns green, and you notice an ABCD Bullish Shield (Green X), you might look for bullish candlestick patterns or moving average crossovers to enter a long trade.
Conversely, if the background turns red and a Super Down Signal appears, it suggests high probability for further downside, giving you strong confirmation to either short BTC or avoid entering new longs.
By combining divergence signals with background colors and the ABCD shields, the Quad Rotation Stochastic provides a layered confirmation system that gives traders greater confidence in their entries and exits — particularly in fast-moving, volatile markets like Bitcoin.
Rainbow Trend IndicatorThis is an indicator based on the MA rainbow concept. It is possible to choose between 15 or 20 MA's and if all 15 MA's is picked, the calculation will be calculated on 15 MA's and if 20 is picked the calculation is calculated on 20 MA's. The indicator will then be a line which is assigned a value from the calculation based on the MA's. If the line is above the dashed zero line, meaning the line's last value is a positive value, the price is in a uptrend and if the line is below the dashed zero line, meaning the line's last value is a negative value, the price is in a downtrend.
In short
If the line is green, the price is in a uptrend. If the line is red, the price is in a downtrend.
Bollinger Bands Ema 50,200,800EMAs converted to Bollinger Bands The bands are 50, 200 and 800 period, forming a strategy and having clear trends and stronger supports and resistances (when the lines converge the area is stronger).
EMA 21,13,8 - scalping3 EMAs will help identify and predict uptrends and downtrends
-If EMAs are all above the candles it a sign to sell & if the EMAs are below its a sign to buy
- If the Green-8 EMA crosses or touches red candle then flips under the other EMAs & candles then it's time to sell
-If the Green-8 EMA crosses or touches green candle then flips above the other EMAs & candles then it's time to buy
- how far is the EMAs from the candle it'll show how strong the trend. combine this strategy with the stochastic oscillator & RSI to get the maximum benefit
GARCH Volume Volatility [MarkitTick]Title: GARCH Volume Volatility
Description
Overview
The GARCH Volume Volatility (GV) indicator is a sophisticated quantitative tool designed to analyze the rate of change in market participation. While the vast majority of technical indicators focus on Price Volatility (how much price moves), this script focuses on Volume Volatility (how unstable the participation is).
Market volume is rarely distributed evenly; it tends to cluster. Periods of high activity are often followed by more high activity, and periods of calm tend to persist. This behavior is known as "heteroskedasticity." This script utilizes an Exponentially Weighted Moving Average (EWMA) model—a core component of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) frameworks—to model these changing variance regimes.
By isolating volume volatility from raw volume data, this tool helps traders distinguish between sustainable liquidity flows and erratic, unsustainable volume shocks that often precede market reversals or breakouts.
Methodology and Calculations
1. Logarithmic vs. Percentage Returns
The foundation of this indicator is the calculation of "Volume Returns"—the period-over-period change in volume.
- The script defaults to Logarithmic Returns. In financial statistics, log returns are preferred because they normalize data that can vary wildly in magnitude (such as cryptocurrency volume spikes), providing a more symmetric view of changes.
- Users can opt for standard percentage changes if they prefer a linear approach.
2. Variance Proxy (Squared Returns)
To measure volatility, the direction of the volume change (up or down) matters less than the magnitude. The script squares the returns to create a "Variance Proxy." This ensures that a massive drop in volume is treated with the same statistical weight as a massive spike in volume—both represent a significant change in the volatility of participation.
3. GARCH-Style Smoothing (EWMA)
Standard Moving Averages (SMA) treat all data points in the lookback period equally. However, volatility is dynamic. This script uses an EWMA model with a tunable "Lambda" (Decay Factor).
- The Recursive Formula: The current calculation relies on a weighted average of the current variance and the previous period's smoothed variance.
- Memory Effect: This allows the indicator to "remember" recent volatility shocks while gradually letting their influence fade. This mimics the GARCH process of conditional variance.
4. Dynamic Statistical Thresholds
The final output is the Volatility (square root of variance). To make this data actionable, the script calculates a dynamic upper and lower limit based on the standard deviation (Z-Score) of the volatility itself over a user-defined lookback period.
How to Use
The indicator plots a histogram that categorizes the market into four distinct volatility regimes:
1. High Volatility (Red Histogram)
Trigger: Volatility > High Band (Upper Standard Deviation).
Interpretation: This signals an extreme anomaly in volume stability. This is not just "high volume," but "erratic volume behavior." This often occurs at:
- Capitulation bottoms (panic selling).
- Euphoric tops (blow-off tops).
- Major news events or earnings releases.
2. Elevated Volatility (Maroon Histogram)
Trigger: Volatility > Mean Average.
Interpretation: The market is in an active state. Participation is changing rapidly, but within statistically normal bounds. This is common during healthy, trending moves where new participants are entering the market steadily.
3. Normal/Low Volatility (Green Histogram)
Trigger: Volatility is within the lower bands.
Interpretation: The market volume is stable. There are no sudden shocks in participation. This is typical of consolidation phases or "creeping" trends where the price drifts without significant volume conviction.
4. Extremely Low Volatility (Bright Green/Transparent)
Trigger: Volatility < Low Band.
Interpretation: The "calm before the storm." When volume volatility collapses to near-zero, it implies that the market has reached a state of equilibrium or disinterest. Historically, volatility is cyclical; periods of extreme compression often lead to violent expansion.
Settings and Configuration
Core Settings
- Use EWMA: When checked (Default), uses the recursive GARCH-style calculation. If unchecked, it reverts to a simple SMA of variance, which is less sensitive to recent shocks but more stable.
- Log Returns: Uses natural log for calculations. Highly recommended for assets with exponential growth or large volume ranges.
- Length: The baseline period for the calculation.
- Threshold Lookback: The number of bars used to calculate the Mean and Standard Deviation bands.
- EWMA Lambda: The decay factor (0.0 to 1.0). A value of 0.94 is standard for risk metrics.
-- Higher Lambda (e.g., 0.98): The indicator reacts slower and is smoother (long memory).
-- Lower Lambda (e.g., 0.80): The indicator reacts very fast to new data (short memory).
Visuals
- Show Thresholds: Toggles the visibility of the statistical bands on the chart.
- High Band (StdDev): The multiplier for the upper warning zone. Default is 1.5 deviations. Increasing this to 2.0 or 3.0 will filter for only the most extreme events.
Disclaimer This tool is for educational and technical analysis purposes only. Breakouts can fail (fake-outs), and past geometric patterns do not guarantee future price action. Always manage risk and use this tool in conjunction with other forms of analysis.
GVWAP_Core (CalendarSpan + EventSpike)GVWAP Core Indicator
General Description (Public)
GVWAP (Generalized Volume-Weighted Average Price) is an advanced anchoring and averaging framework designed to reveal market structure rather than predict price. Unlike traditional VWAP, GVWAP is not limited to volume weighting or session-based anchoring. It can operate on any input series (price, indicators, transforms) and supports multiple weighting schemes, decay behavior, and structural reset logic.
At its core, GVWAP answers a simple question: “Where is the statistically relevant center of activity since the last meaningful structural event?”
The indicator continuously updates a weighted average of the input series, gradually forgetting older data using exponential decay. The anchor point can reset on calendar boundaries (day, week, month, etc.) or on statistically significant events such as abnormal volume spikes. Robust dispersion bands based on mean absolute deviation (MAD) surround the average, providing context for trend, rotation, and compression regimes.
GVWAP is not a trading signal by itself. It is best used as a structural reference layer or as an intermediate transform feeding other indicators, strategies, or regime filters.
Mathematical Description (Quantitative)
Let x_t be an arbitrary input series and w_t a selectable weight function. GVWAP is defined as a normalized exponentially decayed weighted estimator:
GVWAP_t = N_t / D_t
with recursive updates:
N_t = (1 − α)·N_{t−1} + α·w_t·x_t
D_t = (1 − α)·D_{t−1} + α·w_t
where α = 1 − 2^(−1/H) and H is the decay half-life in bars.
Weights may be defined as:
• w_t = V_t (volume)
• w_t = 1 (equal weight)
• w_t = 1 / ATR_t (volatility-normalized)
• w_t = f(n_t) (time-weighted, where n_t is bars since reset)
The estimator resets when a structural condition R_t is satisfied, at which point:
N_t = w_t·x_t, D_t = w_t
For event-based anchoring, volume surprise is computed using a Student‑t–compressed z‑score:
z_t = (V_t − μ_V) / σ_V
tZ_t = z_t / sqrt(1 + z_t² / ν)
A reset occurs when tZ_t exceeds a threshold τ.
Dispersion is measured via a decayed Mean Absolute Deviation:
MAD_t = (Σ λ^{t−i} w_i |x_i − GVWAP_t|) / (Σ λ^{t−i} w_i)
Bands are defined as GVWAP_t ± k·MAD_t.
GVWAP therefore represents a bounded-memory, robust, non‑Gaussian estimator of the local conditional expectation of x_t under dynamic anchoring and weighting.
RastaRasta — Educational Strategy (Pine v5)
Momentum · Smoothing · Trend Study
Overview
The Rasta Strategy is a visual and educational framework designed to help traders study momentum transitions using the interaction between a fast-reacting EMA line and a slower smoothed reference line.
It is not a signal generator or profit system; it’s a learning tool for understanding how smoothing, crossovers, and filters interact under different market conditions.
The script displays:
A primary EMA line (the fast reactive wave).
A Smoothed line (using your chosen smoothing method).
Optional fog zones between them for quick visual context.
Optional DNA rungs connecting both lines to illustrate volatility compression and expansion.
Optional EMA 8 / EMA 21 trend filter to observe higher-time-frame alignment.
Core Idea
The Rasta model focuses on wave interaction. When the fast EMA crosses above the smoothed line, it reflects a shift in short-term momentum relative to background trend pressure. Cross-unders suggest weakening or reversal.
Rather than treating this as a trading “signal,” use it to observe structure, study trend alignment, and test how smoothing type affects reaction speed.
Smoothing Types Explained
The script lets you experiment with multiple smoothing techniques:
Type Description Use Case
SMA (Simple Moving Average) Arithmetic mean of the last n values. Smooth and steady, but slower. Trend-following studies; filters noise on higher time frames.
EMA (Exponential Moving Average) Weights recent data more. Responds faster to new price action. Momentum or reactive strategies; quick shifts and reversals.
RMA (Relative Moving Average) Used internally by RSI; smooths exponentially but slower than EMA. Momentum confirmation; balanced response.
WMA (Weighted Moving Average) Linear weights emphasizing the most recent data strongly. Intraday scalping; crisp but potentially noisy.
None Disables smoothing; uses the EMA line alone. Raw comparison baseline.
Each smoothing method changes how early or late the strategy reacts:
Faster smoothing (EMA/WMA) = more responsive, good for scalping.
Slower smoothing (SMA/RMA) = more stable, good for trend following.
Modes of Study
🔹 Scalper Mode
Use short EMA lengths (e.g., 3–5) and fast smoothing (EMA or WMA).
Focus on 1 min – 15 min charts.
Watch how quick crossovers appear near local tops/bottoms.
Fog and rung compression reveal volatility contraction before bursts.
Goal: study short-term rhythm and liquidity pulses.
🔹 Momentum Mode
Use moderate EMA (5–9) and RMA smoothing.
Ideal for 1 H–4 H charts.
Observe how the fog color aligns with trend shifts.
EMA 8 / 21 filter can act as macro bias; “Enter” labels will appear only in its direction when enabled.
Goal: study sustained motion between pullbacks and acceleration waves.
🔹 Trend-Follower Mode
Use longer EMA (13–21) with SMA smoothing.
Great for daily/weekly charts.
Focus on periods where fog stays unbroken for long stretches — these illustrate clear trend dominance.
Watch rung spacing: tight clusters often precede consolidations; wide rungs signal expanding volatility.
Goal: visualize slow-motion trend transitions and filter whipsaw conditions.
Components
EMA Line (Red): Fast-reacting short-term direction.
Smoothed Line (Yellow): Reference trend baseline.
Fog Zone: Green when EMA > Smoothed (up-momentum), red when below.
DNA Rungs: Thin connectors showing volatility structure.
EMA 8 / 21 Filter (optional):
When enabled, the strategy will only allow Enter events if EMA 8 > EMA 21.
Use this to study higher-trend gating effects.
Educational Applications
Momentum Visualization: Observe how the fast EMA “breathes” around the smoothed baseline.
Trend Transitions: Compare different smoothing types to see how early or late reversals are detected.
Noise Filtering: Experiment with fog opacity and smoothing lengths to understand trade-off between responsiveness and stability.
Risk Concept Simulation: Includes a simple fixed stop-loss parameter (default 13%) for educational demonstrations of position management in the Strategy Tester.
How to Use
Add to Chart → “Strategy.”
Works on any timeframe and instrument.
Adjust Parameters:
Length: base EMA speed.
Smoothing Type: choose SMA, EMA, RMA, or WMA.
Smoothing Length: controls delay and smoothness.
EMA 8 / 21 Filter: toggles trend gating.
Fog & Rungs: visual study options only.
Study Behavior:
Use Strategy Tester → List of Trades for entry/exit context.
Observe how different smoothing types affect early vs. late “Enter” points.
Compare trend periods vs. ranging periods to evaluate efficiency.
Combine with External Tools:
Overlay RSI, MACD, or Volume for deeper correlation analysis.
Use replay mode to visualize crossovers in live sequence.
Interpreting the Labels
Enter: Marks where fast EMA crosses above the smoothed line (or when filter flips positive).
Exit: Marks where fast EMA crosses back below.
These are purely analytical markers — they do not represent trade advice.
Educational Value
The Rasta framework helps learners explore:
Reaction time differences between moving-average algorithms.
Impact of smoothing on signal clarity.
Interaction of local and global trends.
Visualization of volatility contraction (tight DNA rungs) and expansion (wide fog zones).
It’s a sandbox for studying price structure, not a promise of profit.
Disclaimer
This script is provided for educational and research purposes only.
It does not constitute financial advice, trading signals, or performance guarantees. Past market behavior does not predict future outcomes.
Users are encouraged to experiment responsibly, record observations, and develop their own understanding of price behavior.
Author: Michael Culpepper (mikeyc747)
License: Educational / Open for study and modification with credit.
Philosophy:
“Learning the rhythm of the market is more valuable than chasing its profits.” — Rasta
TraderMathLibrary "TraderMath"
A collection of essential trading utilities and mathematical functions used for technical analysis,
including DEMA, Fisher Transform, directional movement, and ADX calculations.
dema(source, length)
Calculates the value of the Double Exponential Moving Average (DEMA).
Parameters:
source (float) : (series int/float) Series of values to process.
length (simple int) : (simple int) Length for the smoothing parameter calculation.
Returns: (float) The double exponentially weighted moving average of the `source`.
roundVal(val)
Constrains a value to the range .
Parameters:
val (float) : (float) Value to constrain.
Returns: (float) Value limited to the range .
fisherTransform(length)
Computes the Fisher Transform oscillator, enhancing turning point sensitivity.
Parameters:
length (int) : (int) Lookback length used to normalize price within the high-low range.
Returns: (float) Fisher Transform value.
dirmov(len)
Calculates the Plus and Minus Directional Movement components (DI+ and DI−).
Parameters:
len (simple int) : (int) Lookback length for directional movement.
Returns: (float ) Array containing .
adx(dilen, adxlen)
Computes the Average Directional Index (ADX) based on DI+ and DI−.
Parameters:
dilen (simple int) : (int) Lookback length for directional movement calculation.
adxlen (simple int) : (int) Smoothing length for ADX computation.
Returns: (float) Average Directional Index value (0–100).
Dynamic Equity Allocation Model"Cash is Trash"? Not Always. Here's Why Science Beats Guesswork.
Every retail trader knows the frustration: you draw support and resistance lines, you spot patterns, you follow market gurus on social media—and still, when the next bear market hits, your portfolio bleeds red. Meanwhile, institutional investors seem to navigate market turbulence with ease, preserving capital when markets crash and participating when they rally. What's their secret?
The answer isn't insider information or access to exotic derivatives. It's systematic, scientifically validated decision-making. While most retail traders rely on subjective chart analysis and emotional reactions, professional portfolio managers use quantitative models that remove emotion from the equation and process multiple streams of market information simultaneously.
This document presents exactly such a system—not a proprietary black box available only to hedge funds, but a fully transparent, academically grounded framework that any serious investor can understand and apply. The Dynamic Equity Allocation Model (DEAM) synthesizes decades of financial research from Nobel laureates and leading academics into a practical tool for tactical asset allocation.
Stop drawing colorful lines on your chart and start thinking like a quant. This isn't about predicting where the market goes next week—it's about systematically adjusting your risk exposure based on what the data actually tells you. When valuations scream danger, when volatility spikes, when credit markets freeze, when multiple warning signals align—that's when cash isn't trash. That's when cash saves your portfolio.
The irony of "cash is trash" rhetoric is that it ignores timing. Yes, being 100% cash for decades would be disastrous. But being 100% equities through every crisis is equally foolish. The sophisticated approach is dynamic: aggressive when conditions favor risk-taking, defensive when they don't. This model shows you how to make that decision systematically, not emotionally.
Whether you're managing your own retirement portfolio or seeking to understand how institutional allocation strategies work, this comprehensive analysis provides the theoretical foundation, mathematical implementation, and practical guidance to elevate your investment approach from amateur to professional.
The choice is yours: keep hoping your chart patterns work out, or start using the same quantitative methods that professionals rely on. The tools are here. The research is cited. The methodology is explained. All you need to do is read, understand, and apply.
The Dynamic Equity Allocation Model (DEAM) is a quantitative framework for systematic allocation between equities and cash, grounded in modern portfolio theory and empirical market research. The model integrates five scientifically validated dimensions of market analysis—market regime, risk metrics, valuation, sentiment, and macroeconomic conditions—to generate dynamic allocation recommendations ranging from 0% to 100% equity exposure. This work documents the theoretical foundations, mathematical implementation, and practical application of this multi-factor approach.
1. Introduction and Theoretical Background
1.1 The Limitations of Static Portfolio Allocation
Traditional portfolio theory, as formulated by Markowitz (1952) in his seminal work "Portfolio Selection," assumes an optimal static allocation where investors distribute their wealth across asset classes according to their risk aversion. This approach rests on the assumption that returns and risks remain constant over time. However, empirical research demonstrates that this assumption does not hold in reality. Fama and French (1989) showed that expected returns vary over time and correlate with macroeconomic variables such as the spread between long-term and short-term interest rates. Campbell and Shiller (1988) demonstrated that the price-earnings ratio possesses predictive power for future stock returns, providing a foundation for dynamic allocation strategies.
The academic literature on tactical asset allocation has evolved considerably over recent decades. Ilmanen (2011) argues in "Expected Returns" that investors can improve their risk-adjusted returns by considering valuation levels, business cycles, and market sentiment. The Dynamic Equity Allocation Model presented here builds on this research tradition and operationalizes these insights into a practically applicable allocation framework.
1.2 Multi-Factor Approaches in Asset Allocation
Modern financial research has shown that different factors capture distinct aspects of market dynamics and together provide a more robust picture of market conditions than individual indicators. Ross (1976) developed the Arbitrage Pricing Theory, a model that employs multiple factors to explain security returns. Following this multi-factor philosophy, DEAM integrates five complementary analytical dimensions, each tapping different information sources and collectively enabling comprehensive market understanding.
2. Data Foundation and Data Quality
2.1 Data Sources Used
The model draws its data exclusively from publicly available market data via the TradingView platform. This transparency and accessibility is a significant advantage over proprietary models that rely on non-public data. The data foundation encompasses several categories of market information, each capturing specific aspects of market dynamics.
First, price data for the S&P 500 Index is obtained through the SPDR S&P 500 ETF (ticker: SPY). The use of a highly liquid ETF instead of the index itself has practical reasons, as ETF data is available in real-time and reflects actual tradability. In addition to closing prices, high, low, and volume data are captured, which are required for calculating advanced volatility measures.
Fundamental corporate metrics are retrieved via TradingView's Financial Data API. These include earnings per share, price-to-earnings ratio, return on equity, debt-to-equity ratio, dividend yield, and share buyback yield. Cochrane (2011) emphasizes in "Presidential Address: Discount Rates" the central importance of valuation metrics for forecasting future returns, making these fundamental data a cornerstone of the model.
Volatility indicators are represented by the CBOE Volatility Index (VIX) and related metrics. The VIX, often referred to as the market's "fear gauge," measures the implied volatility of S&P 500 index options and serves as a proxy for market participants' risk perception. Whaley (2000) describes in "The Investor Fear Gauge" the construction and interpretation of the VIX and its use as a sentiment indicator.
Macroeconomic data includes yield curve information through US Treasury bonds of various maturities and credit risk premiums through the spread between high-yield bonds and risk-free government bonds. These variables capture the macroeconomic conditions and financing conditions relevant for equity valuation. Estrella and Hardouvelis (1991) showed that the shape of the yield curve has predictive power for future economic activity, justifying the inclusion of these data.
2.2 Handling Missing Data
A practical problem when working with financial data is dealing with missing or unavailable values. The model implements a fallback system where a plausible historical average value is stored for each fundamental metric. When current data is unavailable for a specific point in time, this fallback value is used. This approach ensures that the model remains functional even during temporary data outages and avoids systematic biases from missing data. The use of average values as fallback is conservative, as it generates neither overly optimistic nor pessimistic signals.
3. Component 1: Market Regime Detection
3.1 The Concept of Market Regimes
The idea that financial markets exist in different "regimes" or states that differ in their statistical properties has a long tradition in financial science. Hamilton (1989) developed regime-switching models that allow distinguishing between different market states with different return and volatility characteristics. The practical application of this theory consists of identifying the current market state and adjusting portfolio allocation accordingly.
DEAM classifies market regimes using a scoring system that considers three main dimensions: trend strength, volatility level, and drawdown depth. This multidimensional view is more robust than focusing on individual indicators, as it captures various facets of market dynamics. Classification occurs into six distinct regimes: Strong Bull, Bull Market, Neutral, Correction, Bear Market, and Crisis.
3.2 Trend Analysis Through Moving Averages
Moving averages are among the oldest and most widely used technical indicators and have also received attention in academic literature. Brock, Lakonishok, and LeBaron (1992) examined in "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns" the profitability of trading rules based on moving averages and found evidence for their predictive power, although later studies questioned the robustness of these results when considering transaction costs.
The model calculates three moving averages with different time windows: a 20-day average (approximately one trading month), a 50-day average (approximately one quarter), and a 200-day average (approximately one trading year). The relationship of the current price to these averages and the relationship of the averages to each other provide information about trend strength and direction. When the price trades above all three averages and the short-term average is above the long-term, this indicates an established uptrend. The model assigns points based on these constellations, with longer-term trends weighted more heavily as they are considered more persistent.
3.3 Volatility Regimes
Volatility, understood as the standard deviation of returns, is a central concept of financial theory and serves as the primary risk measure. However, research has shown that volatility is not constant but changes over time and occurs in clusters—a phenomenon first documented by Mandelbrot (1963) and later formalized through ARCH and GARCH models (Engle, 1982; Bollerslev, 1986).
DEAM calculates volatility not only through the classic method of return standard deviation but also uses more advanced estimators such as the Parkinson estimator and the Garman-Klass estimator. These methods utilize intraday information (high and low prices) and are more efficient than simple close-to-close volatility estimators. The Parkinson estimator (Parkinson, 1980) uses the range between high and low of a trading day and is based on the recognition that this information reveals more about true volatility than just the closing price difference. The Garman-Klass estimator (Garman and Klass, 1980) extends this approach by additionally considering opening and closing prices.
The calculated volatility is annualized by multiplying it by the square root of 252 (the average number of trading days per year), enabling standardized comparability. The model compares current volatility with the VIX, the implied volatility from option prices. A low VIX (below 15) signals market comfort and increases the regime score, while a high VIX (above 35) indicates market stress and reduces the score. This interpretation follows the empirical observation that elevated volatility is typically associated with falling markets (Schwert, 1989).
3.4 Drawdown Analysis
A drawdown refers to the percentage decline from the highest point (peak) to the lowest point (trough) during a specific period. This metric is psychologically significant for investors as it represents the maximum loss experienced. Calmar (1991) developed the Calmar Ratio, which relates return to maximum drawdown, underscoring the practical relevance of this metric.
The model calculates current drawdown as the percentage distance from the highest price of the last 252 trading days (one year). A drawdown below 3% is considered negligible and maximally increases the regime score. As drawdown increases, the score decreases progressively, with drawdowns above 20% classified as severe and indicating a crisis or bear market regime. These thresholds are empirically motivated by historical market cycles, in which corrections typically encompassed 5-10% drawdowns, bear markets 20-30%, and crises over 30%.
3.5 Regime Classification
Final regime classification occurs through aggregation of scores from trend (40% weight), volatility (30%), and drawdown (30%). The higher weighting of trend reflects the empirical observation that trend-following strategies have historically delivered robust results (Moskowitz, Ooi, and Pedersen, 2012). A total score above 80 signals a strong bull market with established uptrend, low volatility, and minimal losses. At a score below 10, a crisis situation exists requiring defensive positioning. The six regime categories enable a differentiated allocation strategy that not only distinguishes binarily between bullish and bearish but allows gradual gradations.
4. Component 2: Risk-Based Allocation
4.1 Volatility Targeting as Risk Management Approach
The concept of volatility targeting is based on the idea that investors should maximize not returns but risk-adjusted returns. Sharpe (1966, 1994) defined with the Sharpe Ratio the fundamental concept of return per unit of risk, measured as volatility. Volatility targeting goes a step further and adjusts portfolio allocation to achieve constant target volatility. This means that in times of low market volatility, equity allocation is increased, and in times of high volatility, it is reduced.
Moreira and Muir (2017) showed in "Volatility-Managed Portfolios" that strategies that adjust their exposure based on volatility forecasts achieve higher Sharpe Ratios than passive buy-and-hold strategies. DEAM implements this principle by defining a target portfolio volatility (default 12% annualized) and adjusting equity allocation to achieve it. The mathematical foundation is simple: if market volatility is 20% and target volatility is 12%, equity allocation should be 60% (12/20 = 0.6), with the remaining 40% held in cash with zero volatility.
4.2 Market Volatility Calculation
Estimating current market volatility is central to the risk-based allocation approach. The model uses several volatility estimators in parallel and selects the higher value between traditional close-to-close volatility and the Parkinson estimator. This conservative choice ensures the model does not underestimate true volatility, which could lead to excessive risk exposure.
Traditional volatility calculation uses logarithmic returns, as these have mathematically advantageous properties (additive linkage over multiple periods). The logarithmic return is calculated as ln(P_t / P_{t-1}), where P_t is the price at time t. The standard deviation of these returns over a rolling 20-trading-day window is then multiplied by √252 to obtain annualized volatility. This annualization is based on the assumption of independently identically distributed returns, which is an idealization but widely accepted in practice.
The Parkinson estimator uses additional information from the trading range (High minus Low) of each day. The formula is: σ_P = (1/√(4ln2)) × √(1/n × Σln²(H_i/L_i)) × √252, where H_i and L_i are high and low prices. Under ideal conditions, this estimator is approximately five times more efficient than the close-to-close estimator (Parkinson, 1980), as it uses more information per observation.
4.3 Drawdown-Based Position Size Adjustment
In addition to volatility targeting, the model implements drawdown-based risk control. The logic is that deep market declines often signal further losses and therefore justify exposure reduction. This behavior corresponds with the concept of path-dependent risk tolerance: investors who have already suffered losses are typically less willing to take additional risk (Kahneman and Tversky, 1979).
The model defines a maximum portfolio drawdown as a target parameter (default 15%). Since portfolio volatility and portfolio drawdown are proportional to equity allocation (assuming cash has neither volatility nor drawdown), allocation-based control is possible. For example, if the market exhibits a 25% drawdown and target portfolio drawdown is 15%, equity allocation should be at most 60% (15/25).
4.4 Dynamic Risk Adjustment
An advanced feature of DEAM is dynamic adjustment of risk-based allocation through a feedback mechanism. The model continuously estimates what actual portfolio volatility and portfolio drawdown would result at the current allocation. If risk utilization (ratio of actual to target risk) exceeds 1.0, allocation is reduced by an adjustment factor that grows exponentially with overutilization. This implements a form of dynamic feedback that avoids overexposure.
Mathematically, a risk adjustment factor r_adjust is calculated: if risk utilization u > 1, then r_adjust = exp(-0.5 × (u - 1)). This exponential function ensures that moderate overutilization is gently corrected, while strong overutilization triggers drastic reductions. The factor 0.5 in the exponent was empirically calibrated to achieve a balanced ratio between sensitivity and stability.
5. Component 3: Valuation Analysis
5.1 Theoretical Foundations of Fundamental Valuation
DEAM's valuation component is based on the fundamental premise that the intrinsic value of a security is determined by its future cash flows and that deviations between market price and intrinsic value are eventually corrected. Graham and Dodd (1934) established in "Security Analysis" the basic principles of fundamental analysis that remain relevant today. Translated into modern portfolio context, this means that markets with high valuation metrics (high price-earnings ratios) should have lower expected returns than cheaply valued markets.
Campbell and Shiller (1988) developed the Cyclically Adjusted P/E Ratio (CAPE), which smooths earnings over a full business cycle. Their empirical analysis showed that this ratio has significant predictive power for 10-year returns. Asness, Moskowitz, and Pedersen (2013) demonstrated in "Value and Momentum Everywhere" that value effects exist not only in individual stocks but also in asset classes and markets.
5.2 Equity Risk Premium as Central Valuation Metric
The Equity Risk Premium (ERP) is defined as the expected excess return of stocks over risk-free government bonds. It is the theoretical heart of valuation analysis, as it represents the compensation investors demand for bearing equity risk. Damodaran (2012) discusses in "Equity Risk Premiums: Determinants, Estimation and Implications" various methods for ERP estimation.
DEAM calculates ERP not through a single method but combines four complementary approaches with different weights. This multi-method strategy increases estimation robustness and avoids dependence on single, potentially erroneous inputs.
The first method (35% weight) uses earnings yield, calculated as 1/P/E or directly from operating earnings data, and subtracts the 10-year Treasury yield. This method follows Fed Model logic (Yardeni, 2003), although this model has theoretical weaknesses as it does not consistently treat inflation (Asness, 2003).
The second method (30% weight) extends earnings yield by share buyback yield. Share buybacks are a form of capital return to shareholders and increase value per share. Boudoukh et al. (2007) showed in "The Total Shareholder Yield" that the sum of dividend yield and buyback yield is a better predictor of future returns than dividend yield alone.
The third method (20% weight) implements the Gordon Growth Model (Gordon, 1962), which models stock value as the sum of discounted future dividends. Under constant growth g assumption: Expected Return = Dividend Yield + g. The model estimates sustainable growth as g = ROE × (1 - Payout Ratio), where ROE is return on equity and payout ratio is the ratio of dividends to earnings. This formula follows from equity theory: unretained earnings are reinvested at ROE and generate additional earnings growth.
The fourth method (15% weight) combines total shareholder yield (Dividend + Buybacks) with implied growth derived from revenue growth. This method considers that companies with strong revenue growth should generate higher future earnings, even if current valuations do not yet fully reflect this.
The final ERP is the weighted average of these four methods. A high ERP (above 4%) signals attractive valuations and increases the valuation score to 95 out of 100 possible points. A negative ERP, where stocks have lower expected returns than bonds, results in a minimal score of 10.
5.3 Quality Adjustments to Valuation
Valuation metrics alone can be misleading if not interpreted in the context of company quality. A company with a low P/E may be cheap or fundamentally problematic. The model therefore implements quality adjustments based on growth, profitability, and capital structure.
Revenue growth above 10% annually adds 10 points to the valuation score, moderate growth above 5% adds 5 points. This adjustment reflects that growth has independent value (Modigliani and Miller, 1961, extended by later growth theory). Net margin above 15% signals pricing power and operational efficiency and increases the score by 5 points, while low margins below 8% indicate competitive pressure and subtract 5 points.
Return on equity (ROE) above 20% characterizes outstanding capital efficiency and increases the score by 5 points. Piotroski (2000) showed in "Value Investing: The Use of Historical Financial Statement Information" that fundamental quality signals such as high ROE can improve the performance of value strategies.
Capital structure is evaluated through the debt-to-equity ratio. A conservative ratio below 1.0 multiplies the valuation score by 1.2, while high leverage above 2.0 applies a multiplier of 0.8. This adjustment reflects that high debt constrains financial flexibility and can become problematic in crisis times (Korteweg, 2010).
6. Component 4: Sentiment Analysis
6.1 The Role of Sentiment in Financial Markets
Investor sentiment, defined as the collective psychological attitude of market participants, influences asset prices independently of fundamental data. Baker and Wurgler (2006, 2007) developed a sentiment index and showed that periods of high sentiment are followed by overvaluations that later correct. This insight justifies integrating a sentiment component into allocation decisions.
Sentiment is difficult to measure directly but can be proxied through market indicators. The VIX is the most widely used sentiment indicator, as it aggregates implied volatility from option prices. High VIX values reflect elevated uncertainty and risk aversion, while low values signal market comfort. Whaley (2009) refers to the VIX as the "Investor Fear Gauge" and documents its role as a contrarian indicator: extremely high values typically occur at market bottoms, while low values occur at tops.
6.2 VIX-Based Sentiment Assessment
DEAM uses statistical normalization of the VIX by calculating the Z-score: z = (VIX_current - VIX_average) / VIX_standard_deviation. The Z-score indicates how many standard deviations the current VIX is from the historical average. This approach is more robust than absolute thresholds, as it adapts to the average volatility level, which can vary over longer periods.
A Z-score below -1.5 (VIX is 1.5 standard deviations below average) signals exceptionally low risk perception and adds 40 points to the sentiment score. This may seem counterintuitive—shouldn't low fear be bullish? However, the logic follows the contrarian principle: when no one is afraid, everyone is already invested, and there is limited further upside potential (Zweig, 1973). Conversely, a Z-score above 1.5 (extreme fear) adds -40 points, reflecting market panic but simultaneously suggesting potential buying opportunities.
6.3 VIX Term Structure as Sentiment Signal
The VIX term structure provides additional sentiment information. Normally, the VIX trades in contango, meaning longer-term VIX futures have higher prices than short-term. This reflects that short-term volatility is currently known, while long-term volatility is more uncertain and carries a risk premium. The model compares the VIX with VIX9D (9-day volatility) and identifies backwardation (VIX > 1.05 × VIX9D) and steep backwardation (VIX > 1.15 × VIX9D).
Backwardation occurs when short-term implied volatility is higher than longer-term, which typically happens during market stress. Investors anticipate immediate turbulence but expect calming. Psychologically, this reflects acute fear. The model subtracts 15 points for backwardation and 30 for steep backwardation, as these constellations signal elevated risk. Simon and Wiggins (2001) analyzed the VIX futures curve and showed that backwardation is associated with market declines.
6.4 Safe-Haven Flows
During crisis times, investors flee from risky assets into safe havens: gold, US dollar, and Japanese yen. This "flight to quality" is a sentiment signal. The model calculates the performance of these assets relative to stocks over the last 20 trading days. When gold or the dollar strongly rise while stocks fall, this indicates elevated risk aversion.
The safe-haven component is calculated as the difference between safe-haven performance and stock performance. Positive values (safe havens outperform) subtract up to 20 points from the sentiment score, negative values (stocks outperform) add up to 10 points. The asymmetric treatment (larger deduction for risk-off than bonus for risk-on) reflects that risk-off movements are typically sharper and more informative than risk-on phases.
Baur and Lucey (2010) examined safe-haven properties of gold and showed that gold indeed exhibits negative correlation with stocks during extreme market movements, confirming its role as crisis protection.
7. Component 5: Macroeconomic Analysis
7.1 The Yield Curve as Economic Indicator
The yield curve, represented as yields of government bonds of various maturities, contains aggregated expectations about future interest rates, inflation, and economic growth. The slope of the yield curve has remarkable predictive power for recessions. Estrella and Mishkin (1998) showed that an inverted yield curve (short-term rates higher than long-term) predicts recessions with high reliability. This is because inverted curves reflect restrictive monetary policy: the central bank raises short-term rates to combat inflation, dampening economic activity.
DEAM calculates two spread measures: the 2-year-minus-10-year spread and the 3-month-minus-10-year spread. A steep, positive curve (spreads above 1.5% and 2% respectively) signals healthy growth expectations and generates the maximum yield curve score of 40 points. A flat curve (spreads near zero) reduces the score to 20 points. An inverted curve (negative spreads) is particularly alarming and results in only 10 points.
The choice of two different spreads increases analysis robustness. The 2-10 spread is most established in academic literature, while the 3M-10Y spread is often considered more sensitive, as the 3-month rate directly reflects current monetary policy (Ang, Piazzesi, and Wei, 2006).
7.2 Credit Conditions and Spreads
Credit spreads—the yield difference between risky corporate bonds and safe government bonds—reflect risk perception in the credit market. Gilchrist and Zakrajšek (2012) constructed an "Excess Bond Premium" that measures the component of credit spreads not explained by fundamentals and showed this is a predictor of future economic activity and stock returns.
The model approximates credit spread by comparing the yield of high-yield bond ETFs (HYG) with investment-grade bond ETFs (LQD). A narrow spread below 200 basis points signals healthy credit conditions and risk appetite, contributing 30 points to the macro score. Very wide spreads above 1000 basis points (as during the 2008 financial crisis) signal credit crunch and generate zero points.
Additionally, the model evaluates whether "flight to quality" is occurring, identified through strong performance of Treasury bonds (TLT) with simultaneous weakness in high-yield bonds. This constellation indicates elevated risk aversion and reduces the credit conditions score.
7.3 Financial Stability at Corporate Level
While the yield curve and credit spreads reflect macroeconomic conditions, financial stability evaluates the health of companies themselves. The model uses the aggregated debt-to-equity ratio and return on equity of the S&P 500 as proxies for corporate health.
A low leverage level below 0.5 combined with high ROE above 15% signals robust corporate balance sheets and generates 20 points. This combination is particularly valuable as it represents both defensive strength (low debt means crisis resistance) and offensive strength (high ROE means earnings power). High leverage above 1.5 generates only 5 points, as it implies vulnerability to interest rate increases and recessions.
Korteweg (2010) showed in "The Net Benefits to Leverage" that optimal debt maximizes firm value, but excessive debt increases distress costs. At the aggregated market level, high debt indicates fragilities that can become problematic during stress phases.
8. Component 6: Crisis Detection
8.1 The Need for Systematic Crisis Detection
Financial crises are rare but extremely impactful events that suspend normal statistical relationships. During normal market volatility, diversified portfolios and traditional risk management approaches function, but during systemic crises, seemingly independent assets suddenly correlate strongly, and losses exceed historical expectations (Longin and Solnik, 2001). This justifies a separate crisis detection mechanism that operates independently of regular allocation components.
Reinhart and Rogoff (2009) documented in "This Time Is Different: Eight Centuries of Financial Folly" recurring patterns in financial crises: extreme volatility, massive drawdowns, credit market dysfunction, and asset price collapse. DEAM operationalizes these patterns into quantifiable crisis indicators.
8.2 Multi-Signal Crisis Identification
The model uses a counter-based approach where various stress signals are identified and aggregated. This methodology is more robust than relying on a single indicator, as true crises typically occur simultaneously across multiple dimensions. A single signal may be a false alarm, but the simultaneous presence of multiple signals increases confidence.
The first indicator is a VIX above the crisis threshold (default 40), adding one point. A VIX above 60 (as in 2008 and March 2020) adds two additional points, as such extreme values are historically very rare. This tiered approach captures the intensity of volatility.
The second indicator is market drawdown. A drawdown above 15% adds one point, as corrections of this magnitude can be potential harbingers of larger crises. A drawdown above 25% adds another point, as historical bear markets typically encompass 25-40% drawdowns.
The third indicator is credit market spreads above 500 basis points, adding one point. Such wide spreads occur only during significant credit market disruptions, as in 2008 during the Lehman crisis.
The fourth indicator identifies simultaneous losses in stocks and bonds. Normally, Treasury bonds act as a hedge against equity risk (negative correlation), but when both fall simultaneously, this indicates systemic liquidity problems or inflation/stagflation fears. The model checks whether both SPY and TLT have fallen more than 10% and 5% respectively over 5 trading days, adding two points.
The fifth indicator is a volume spike combined with negative returns. Extreme trading volumes (above twice the 20-day average) with falling prices signal panic selling. This adds one point.
A crisis situation is diagnosed when at least 3 indicators trigger, a severe crisis at 5 or more indicators. These thresholds were calibrated through historical backtesting to identify true crises (2008, 2020) without generating excessive false alarms.
8.3 Crisis-Based Allocation Override
When a crisis is detected, the system overrides the normal allocation recommendation and caps equity allocation at maximum 25%. In a severe crisis, the cap is set at 10%. This drastic defensive posture follows the empirical observation that crises typically require time to develop and that early reduction can avoid substantial losses (Faber, 2007).
This override logic implements a "safety first" principle: in situations of existential danger to the portfolio, capital preservation becomes the top priority. Roy (1952) formalized this approach in "Safety First and the Holding of Assets," arguing that investors should primarily minimize ruin probability.
9. Integration and Final Allocation Calculation
9.1 Component Weighting
The final allocation recommendation emerges through weighted aggregation of the five components. The standard weighting is: Market Regime 35%, Risk Management 25%, Valuation 20%, Sentiment 15%, Macro 5%. These weights reflect both theoretical considerations and empirical backtesting results.
The highest weighting of market regime is based on evidence that trend-following and momentum strategies have delivered robust results across various asset classes and time periods (Moskowitz, Ooi, and Pedersen, 2012). Current market momentum is highly informative for the near future, although it provides no information about long-term expectations.
The substantial weighting of risk management (25%) follows from the central importance of risk control. Wealth preservation is the foundation of long-term wealth creation, and systematic risk management is demonstrably value-creating (Moreira and Muir, 2017).
The valuation component receives 20% weight, based on the long-term mean reversion of valuation metrics. While valuation has limited short-term predictive power (bull and bear markets can begin at any valuation), the long-term relationship between valuation and returns is robustly documented (Campbell and Shiller, 1988).
Sentiment (15%) and Macro (5%) receive lower weights, as these factors are subtler and harder to measure. Sentiment is valuable as a contrarian indicator at extremes but less informative in normal ranges. Macro variables such as the yield curve have strong predictive power for recessions, but the transmission from recessions to stock market performance is complex and temporally variable.
9.2 Model Type Adjustments
DEAM allows users to choose between four model types: Conservative, Balanced, Aggressive, and Adaptive. This choice modifies the final allocation through additive adjustments.
Conservative mode subtracts 10 percentage points from allocation, resulting in consistently more cautious positioning. This is suitable for risk-averse investors or those with limited investment horizons. Aggressive mode adds 10 percentage points, suitable for risk-tolerant investors with long horizons.
Adaptive mode implements procyclical adjustment based on short-term momentum: if the market has risen more than 5% in the last 20 days, 5 percentage points are added; if it has declined more than 5%, 5 points are subtracted. This logic follows the observation that short-term momentum persists (Jegadeesh and Titman, 1993), but the moderate size of adjustment avoids excessive timing bets.
Balanced mode makes no adjustment and uses raw model output. This neutral setting is suitable for investors who wish to trust model recommendations unchanged.
9.3 Smoothing and Stability
The allocation resulting from aggregation undergoes final smoothing through a simple moving average over 3 periods. This smoothing is crucial for model practicality, as it reduces frequent trading and thus transaction costs. Without smoothing, the model could fluctuate between adjacent allocations with every small input change.
The choice of 3 periods as smoothing window is a compromise between responsiveness and stability. Longer smoothing would excessively delay signals and impede response to true regime changes. Shorter or no smoothing would allow too much noise. Empirical tests showed that 3-period smoothing offers an optimal ratio between these goals.
10. Visualization and Interpretation
10.1 Main Output: Equity Allocation
DEAM's primary output is a time series from 0 to 100 representing the recommended percentage allocation to equities. This representation is intuitive: 100% means full investment in stocks (specifically: an S&P 500 ETF), 0% means complete cash position, and intermediate values correspond to mixed portfolios. A value of 60% means, for example: invest 60% of wealth in SPY, hold 40% in money market instruments or cash.
The time series is color-coded to enable quick visual interpretation. Green shades represent high allocations (above 80%, bullish), red shades low allocations (below 20%, bearish), and neutral colors middle allocations. The chart background is dynamically colored based on the signal, enhancing readability in different market phases.
10.2 Dashboard Metrics
A tabular dashboard presents key metrics compactly. This includes current allocation, cash allocation (complement), an aggregated signal (BULLISH/NEUTRAL/BEARISH), current market regime, VIX level, market drawdown, and crisis status.
Additionally, fundamental metrics are displayed: P/E Ratio, Equity Risk Premium, Return on Equity, Debt-to-Equity Ratio, and Total Shareholder Yield. This transparency allows users to understand model decisions and form their own assessments.
Component scores (Regime, Risk, Valuation, Sentiment, Macro) are also displayed, each normalized on a 0-100 scale. This shows which factors primarily drive the current recommendation. If, for example, the Risk score is very low (20) while other scores are moderate (50-60), this indicates that risk management considerations are pulling allocation down.
10.3 Component Breakdown (Optional)
Advanced users can display individual components as separate lines in the chart. This enables analysis of component dynamics: do all components move synchronously, or are there divergences? Divergences can be particularly informative. If, for example, the market regime is bullish (high score) but the valuation component is very negative, this signals an overbought market not fundamentally supported—a classic "bubble warning."
This feature is disabled by default to keep the chart clean but can be activated for deeper analysis.
10.4 Confidence Bands
The model optionally displays uncertainty bands around the main allocation line. These are calculated as ±1 standard deviation of allocation over a rolling 20-period window. Wide bands indicate high volatility of model recommendations, suggesting uncertain market conditions. Narrow bands indicate stable recommendations.
This visualization implements a concept of epistemic uncertainty—uncertainty about the model estimate itself, not just market volatility. In phases where various indicators send conflicting signals, the allocation recommendation becomes more volatile, manifesting in wider bands. Users can understand this as a warning to act more cautiously or consult alternative information sources.
11. Alert System
11.1 Allocation Alerts
DEAM implements an alert system that notifies users of significant events. Allocation alerts trigger when smoothed allocation crosses certain thresholds. An alert is generated when allocation reaches 80% (from below), signaling strong bullish conditions. Another alert triggers when allocation falls to 20%, indicating defensive positioning.
These thresholds are not arbitrary but correspond with boundaries between model regimes. An allocation of 80% roughly corresponds to a clear bull market regime, while 20% corresponds to a bear market regime. Alerts at these points are therefore informative about fundamental regime shifts.
11.2 Crisis Alerts
Separate alerts trigger upon detection of crisis and severe crisis. These alerts have highest priority as they signal large risks. A crisis alert should prompt investors to review their portfolio and potentially take defensive measures beyond the automatic model recommendation (e.g., hedging through put options, rebalancing to more defensive sectors).
11.3 Regime Change Alerts
An alert triggers upon change of market regime (e.g., from Neutral to Correction, or from Bull Market to Strong Bull). Regime changes are highly informative events that typically entail substantial allocation changes. These alerts enable investors to proactively respond to changes in market dynamics.
11.4 Risk Breach Alerts
A specialized alert triggers when actual portfolio risk utilization exceeds target parameters by 20%. This is a warning signal that the risk management system is reaching its limits, possibly because market volatility is rising faster than allocation can be reduced. In such situations, investors should consider manual interventions.
12. Practical Application and Limitations
12.1 Portfolio Implementation
DEAM generates a recommendation for allocation between equities (S&P 500) and cash. Implementation by an investor can take various forms. The most direct method is using an S&P 500 ETF (e.g., SPY, VOO) for equity allocation and a money market fund or savings account for cash allocation.
A rebalancing strategy is required to synchronize actual allocation with model recommendation. Two approaches are possible: (1) rule-based rebalancing at every 10% deviation between actual and target, or (2) time-based monthly rebalancing. Both have trade-offs between responsiveness and transaction costs. Empirical evidence (Jaconetti, Kinniry, and Zilbering, 2010) suggests rebalancing frequency has moderate impact on performance, and investors should optimize based on their transaction costs.
12.2 Adaptation to Individual Preferences
The model offers numerous adjustment parameters. Component weights can be modified if investors place more or less belief in certain factors. A fundamentally-oriented investor might increase valuation weight, while a technical trader might increase regime weight.
Risk target parameters (target volatility, max drawdown) should be adapted to individual risk tolerance. Younger investors with long investment horizons can choose higher target volatility (15-18%), while retirees may prefer lower volatility (8-10%). This adjustment systematically shifts average equity allocation.
Crisis thresholds can be adjusted based on preference for sensitivity versus specificity of crisis detection. Lower thresholds (e.g., VIX > 35 instead of 40) increase sensitivity (more crises are detected) but reduce specificity (more false alarms). Higher thresholds have the reverse effect.
12.3 Limitations and Disclaimers
DEAM is based on historical relationships between indicators and market performance. There is no guarantee these relationships will persist in the future. Structural changes in markets (e.g., through regulation, technology, or central bank policy) can break established patterns. This is the fundamental problem of induction in financial science (Taleb, 2007).
The model is optimized for US equities (S&P 500). Application to other markets (international stocks, bonds, commodities) would require recalibration. The indicators and thresholds are specific to the statistical properties of the US equity market.
The model cannot eliminate losses. Even with perfect crisis prediction, an investor following the model would lose money in bear markets—just less than a buy-and-hold investor. The goal is risk-adjusted performance improvement, not risk elimination.
Transaction costs are not modeled. In practice, spreads, commissions, and taxes reduce net returns. Frequent trading can cause substantial costs. Model smoothing helps minimize this, but users should consider their specific cost situation.
The model reacts to information; it does not anticipate it. During sudden shocks (e.g., 9/11, COVID-19 lockdowns), the model can only react after price movements, not before. This limitation is inherent to all reactive systems.
12.4 Relationship to Other Strategies
DEAM is a tactical asset allocation approach and should be viewed as a complement, not replacement, for strategic asset allocation. Brinson, Hood, and Beebower (1986) showed in their influential study "Determinants of Portfolio Performance" that strategic asset allocation (long-term policy allocation) explains the majority of portfolio performance, but this leaves room for tactical adjustments based on market timing.
The model can be combined with value and momentum strategies at the individual stock level. While DEAM controls overall market exposure, within-equity decisions can be optimized through stock-picking models. This separation between strategic (market exposure) and tactical (stock selection) levels follows classical portfolio theory.
The model does not replace diversification across asset classes. A complete portfolio should also include bonds, international stocks, real estate, and alternative investments. DEAM addresses only the US equity allocation decision within a broader portfolio.
13. Scientific Foundation and Evaluation
13.1 Theoretical Consistency
DEAM's components are based on established financial theory and empirical evidence. The market regime component follows from regime-switching models (Hamilton, 1989) and trend-following literature. The risk management component implements volatility targeting (Moreira and Muir, 2017) and modern portfolio theory (Markowitz, 1952). The valuation component is based on discounted cash flow theory and empirical value research (Campbell and Shiller, 1988; Fama and French, 1992). The sentiment component integrates behavioral finance (Baker and Wurgler, 2006). The macro component uses established business cycle indicators (Estrella and Mishkin, 1998).
This theoretical grounding distinguishes DEAM from purely data-mining-based approaches that identify patterns without causal theory. Theory-guided models have greater probability of functioning out-of-sample, as they are based on fundamental mechanisms, not random correlations (Lo and MacKinlay, 1990).
13.2 Empirical Validation
While this document does not present detailed backtest analysis, it should be noted that rigorous validation of a tactical asset allocation model should include several elements:
In-sample testing establishes whether the model functions at all in the data on which it was calibrated. Out-of-sample testing is crucial: the model should be tested in time periods not used for development. Walk-forward analysis, where the model is successively trained on rolling windows and tested in the next window, approximates real implementation.
Performance metrics should be risk-adjusted. Pure return consideration is misleading, as higher returns often only compensate for higher risk. Sharpe Ratio, Sortino Ratio, Calmar Ratio, and Maximum Drawdown are relevant metrics. Comparison with benchmarks (Buy-and-Hold S&P 500, 60/40 Stock/Bond portfolio) contextualizes performance.
Robustness checks test sensitivity to parameter variation. If the model only functions at specific parameter settings, this indicates overfitting. Robust models show consistent performance over a range of plausible parameters.
13.3 Comparison with Existing Literature
DEAM fits into the broader literature on tactical asset allocation. Faber (2007) presented a simple momentum-based timing system that goes long when the market is above its 10-month average, otherwise cash. This simple system avoided large drawdowns in bear markets. DEAM can be understood as a sophistication of this approach that integrates multiple information sources.
Ilmanen (2011) discusses various timing factors in "Expected Returns" and argues for multi-factor approaches. DEAM operationalizes this philosophy. Asness, Moskowitz, and Pedersen (2013) showed that value and momentum effects work across asset classes, justifying cross-asset application of regime and valuation signals.
Ang (2014) emphasizes in "Asset Management: A Systematic Approach to Factor Investing" the importance of systematic, rule-based approaches over discretionary decisions. DEAM is fully systematic and eliminates emotional biases that plague individual investors (overconfidence, hindsight bias, loss aversion).
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BTC Power Law Valuation BandsBTC Power Law Rainbow
A long-term valuation framework for Bitcoin based on Power Law growth — designed to help identify macro accumulation and distribution zones, aligned with long-term investor behavior.
🔍 What Is a Power Law?
A Power Law is a mathematical relationship where one quantity varies as a power of another. In this model:
Price ≈ a × (Time)^b
It captures the non-linear, exponentially slowing growth of Bitcoin over time. Rather than using linear or cyclical models, this approach aligns with how complex systems, such as networks or monetary adoption curves, often grow — rapidly at first, and then more slowly, but persistently.
🧠 Why Power Law for BTC?
Bitcoin:
Has finite supply and increasing adoption.
Operates as a monetary network , where Metcalfe’s Law and power laws naturally emerge.
Exhibits exponential growth over logarithmic time when viewed on a log-log chart .
This makes it uniquely well-suited for power law modeling.
🌈 How to Use the Valuation Bands
The central white line represents the modeled fair value according to the power law.
Colored bands represent deviations from the model in logarithmic space, acting as macro zones:
🔵 Lower Bands: Deep value / Accumulation zones.
🟡 Mid Bands: Fair value.
🔴 Upper Bands: Euphoria / Risk of macro tops.
📐 Smart Money Concepts (SMC) Alignment
Accumulation: Occurs when price consolidates near lower bands — often aligning with institutional positioning.
Markup: As price re-enters or ascends the bands, we often see breakout behavior and trend expansion.
Distribution: When price extends above upper bands, potential for exit liquidity creation and distribution events.
Reversion: Historically, price mean-reverts toward the model — rarely staying outside the bands for long.
This makes the model useful for:
Cycle timing
Long-term DCA strategy zones
Identifying value dislocations
Filtering short-term noise
⚠️ Disclaimer
This tool is for educational and informational purposes only . It is not financial advice. The power law model is a non-predictive, mathematical framework and does not guarantee future price movements .
Always use additional tools, risk management, and your own judgment before making trading or investment decisions.
