Returns Stationarity Analysis (YavuzAkbay)This indicator analyzes the stationarity of a stock's price returns over time. Stationarity is an important property of time series data, as it determines the validity of statistical analysis and forecasting methods.
The indicator provides several visual cues to help assess the stationarity of the price returns:
Price Returns: Displays the daily percentage change in the stock's closing price.
Moving Average: Shows the smoothed trend of the price returns using a simple moving average.
Z-Score: Calculates the standardized z-score of the price returns, highlighting periods of significant deviation from the mean.
Autocorrelation: Plots the autocorrelation of the price returns, which measures the persistence or "memory" in the time series. High autocorrelation suggests non-stationarity.
The indicator also includes the following features:
Customizable lookback period and smoothing window for the moving statistics.
Lag parameter for the autocorrelation calculation.
Shaded bands to indicate the significance levels for the z-score and autocorrelation.
Visual signals (red dots) to highlight periods that are potentially non-stationary, based on a combination of high z-score and autocorrelation.
Informative labels to guide the interpretation of the results.
This indicator can be a useful tool for stock market analysts and traders to identify potential changes in the underlying dynamics of a stock's price behavior, which may have implications for forecasting, risk management, and investment strategies.
Autocorrelation
Dynamic Autocorrelation Visualizer (YavuzAkbay)The Dynamic Autocorrelation Visualizer (DAV) is a specialized indicator that analyzes and displays the autocorrelation of closing prices over multiple time lags. The autocorrelation function is a well-established economic calculation that measures how past price movements correlate with current prices at various intervals. This indicator implements this function to provide traders with insights into how these correlations evolve over time, enabling them to identify shifts in market behavior and trends.
Key Features and Functionality
1. Input Parameters:
Max Lag: This parameter determines the maximum number of lags for which the autocorrelation will be calculated. By default, it is set to 10, allowing traders to observe the correlation from the most recent price up to 10 periods back.
Calculation Period: The period over which the autocorrelation is calculated, set by default to 50. This setting allows users to adapt the analysis to different time frames depending on their trading strategies.
2. Autocorrelation Calculation:
The DAV calculates the average closing price over the specified period using the Simple Moving Average (SMA). This average serves as a reference point for measuring deviations in price behavior.
It then computes the denominator for the autocorrelation formula, which is the sum of the squared differences between each closing price and the average price. This normalization ensures that the autocorrelation values are meaningful and statistically valid.
For each specified lag (from 0 to max_lag - 1), the indicator calculates the numerator by summing the product of deviations from the mean for both the current and lagged prices. The autocorrelation value for each lag is then derived by dividing the numerator by the denominator, producing a set of autocorrelation values that reflect the strength and direction of price relationships over time.
3. Visualization:
The results for each lag's autocorrelation are plotted as individual lines on the chart, each differentiated by color to represent different lag periods.
A zero line is drawn as a reference, helping traders easily identify when autocorrelation values cross from positive to negative or vice versa.
The color gradient from the brightest blue (for lag 1) to darker shades indicates the relative strength of the autocorrelation for each lag, providing an immediate visual cue for analysis.
Indicator is Useful for
Seeing how correlation patterns evolve
Identifying periods where the market changes its behavior
Spotting when certain lag patterns become more or less significant
How to Use the DAV Indicator
Before using the indicator, it should be backtested on the chart and the mechanics should be learned. In general, if all lags of the indicator are above 0, it means that the trend is continuing. When the lags start to fall below 0 one by one, it means a trend reversal or instability. The indicator is in a sense a 90 degree freeze trace of the Autocorrelation indicator that I have also integrated into Tradingview (available in my profile), so it may be more understandable if used in conjunction with this indicator.
Autocorrelogram (YavuzAkbay)The Autocorrelogram (ACF) is a statistical tool designed for traders and analysts to evaluate the autocorrelation of price movements over time. Autocorrelation measures the correlation of a signal with a delayed version of itself, providing insights into the degree to which past price movements influence future price movements. This indicator is particularly useful for identifying trends and patterns in time series data, helping traders make informed decisions based on historical price behavior.
Key Components and Functionality
1. Input Parameters:
Sample Size: This parameter defines the number of data points used in the calculation of the autocorrelation function. A minimum value of 9 ensures statistical relevance. The default value is set to 100, which provides a broad view of the price behavior.
Data Source: Users can select the price data they wish to analyze (e.g., closing prices). This flexibility allows traders to apply the ACF to various price types, depending on their trading strategy.
Significance Level: This parameter determines the threshold for statistical significance in the autocorrelation values. The default value is set at 1.96, corresponding to a 95% confidence level, but users can adjust it to their preferences.
Calculate Change: This boolean option allows users to choose whether to calculate the change in the selected data source (e.g., daily price changes) rather than using the raw data. Analyzing changes can highlight momentum shifts that may be obscured in absolute price levels.
2. Core Calculations:
Simple Moving Average (SMA): The indicator computes the SMA of the selected data source over the defined sample size. This average serves as a baseline for assessing deviations in price behavior.
Variance Calculation: The variance of the price changes is calculated to understand the spread of the data. The variance is scaled by the sample size to ensure that the autocorrelation values are appropriately normalized.
Lag Value: The indicator calculates a lag value based on the sample size to determine how many periods back the autocorrelation will be calculated. This helps in assessing correlations at different time intervals.
3. Autocorrelation Calculation:
The script calculates the autocorrelation for lags ranging from 0 to 53. For each lag, it computes the autocovariance (the correlation of the signal with itself at different time intervals) and normalizes this by the variance. The result is a set of autocorrelation values that indicate the strength and direction of the relationship between current and past price movements.
4. Visualization:
The autocorrelation values are plotted as lines on the chart, with different colors indicating positive and negative correlations. Lines are dynamically drawn for each lag, providing a visual representation of how past prices influence current prices. A maximum of 54 lines (for lags 0 to 53) is maintained, with the oldest line being removed when the limit is exceeded.
Significance Levels: Horizontal lines are drawn at the defined significance levels, helping traders quickly identify when the autocorrelation values exceed the statistically significant threshold. These lines serve as benchmarks for interpreting the relevance of the autocorrelation values.
How to Use the ACF Indicator
Identifying Trends: Traders can use the ACF indicator to spot trends in the data. Strong positive autocorrelation at a given lag indicates that past price movements have a lasting influence on future movements, suggesting a potential continuation of the current trend. Conversely, significant negative autocorrelation may indicate reversals or mean reversion.
Decision Making: By comparing the autocorrelation values against the significance levels, traders can make informed decisions. For example, if the autocorrelation at lag 1 is significantly positive, it may suggest that a trend is likely to persist in the immediate future, prompting traders to consider long positions.
Setting Parameters: Adjusting the sample size and significance level allows traders to tailor the indicator to their specific market conditions and trading style. A larger sample size may provide more stable estimates but could obscure short-term fluctuations, while a smaller size may capture quick changes but with higher variability.
Combining with Other Indicators: The ACF can be used in conjunction with other technical indicators (like Moving Averages or RSI) to enhance trading strategies. Confirming signals from multiple indicators can provide stronger trade confirmations.
AutocorrelationWhat is Autocorrelation?
Autocorrelation is a mathematical concept used to measure the degree of similarity between a given time series and a lagged version of itself over successive time intervals. Mathematically, it is the correlation of a signal with a delayed copy of itself as a function of delay. In simpler terms, autocorrelation helps us understand whether and how past values in a time series are related to future values.
Autocorrelation in Finance:
In finance, the autocorrelation is a tool used to analyze the behavior of time series data, such as asset prices or returns. It can reveal "patterns", trends, or cycles within the data.
Price Autocorrelation: When applied to prices, autocorrelations can indicate whether an asset price tends to follow a trend. On price you will typically observe positive autocorrelation because price often exhibits a momentum effect where today's price is positively correlated with past prices. As a result, when prices are trending, they tend to continue in the same direction, creating a positive autocorrelation.
Returns Autocorrelation: Returns on the other hand, generally show less autocorrelation than prices. This is because returns represent the change in prices over time, and in efficient markets, returns are often modeled as a random walk, leading to low or no significant autocorrelation. However, under certain market conditions, you may observe positive or negative autocorrelation in returns. Positive Autocorrelation of returns indicates a trend effect, where past returns can predict future returns. Negative Returns Autocorrelation suggest mean reversion, where large positive returns are often followed by negative returns and vice versa.
Critical Value Analysis:
This indicator comes with critical values based on user-selected confidence levels (90%,95%,99%). It assesses whether the autocorrelation at a particular lag is statistically significant, which is crucial for distinguishing between random noise and meaningful events.
Trading Based on Autocorrelation:
While this indicator was not really developed to be directly used for trading, this indicator is was instead to raise awareness on why you should avoid strategies involving mean reversion on price.
Price Scenarios - The Quant ScienceGENERAL OVERVIEW
Price Scenarios - The Quant Science is a quantitative statistical indicator that provides a forecast probability about future prices moving using the mathematical-statistical formula of statistical probability and expected value.
HOW TO USE
The indicator displays arrow-shaped signals that represent the probable future price movement calculated by the indicator, including the current percentage probability. Additionally, the candlesticks are colored based on the predicted direction to facilitate visual analysis. By default, green is used for bullish movements and red for bearish movements. The trader can set the analysis period (default value is 200) and the percentage threshold of probability to consider (default value is greater than 0.50 or 50%) through the user interface.
USER INTERFACE
Lenght analysis: with this features you can handle the length of the dataset to be used for estimating statistical probabilities.
Expected value: with this feature you can handle the threshold of the expected value to filter, only probabilities greater than this threshold will be considered by the model. By default, it is set to 0.50, which is equivalent to 50%.
Design Settings: modify the colors of your indicator with just a few clicks by managing this function.
We recommend disabling 'Wick' and 'Border' from the settings panel for a smoother and more efficient user experience.
[Excalibur] Ehlers AutoCorrelation Periodogram ModifiedKeep your coins folks, I don't need them, don't want them. If you wish be generous, I do hope that charitable peoples worldwide with surplus food stocks may consider stocking local food banks before stuffing monetary bank vaults, for the crusade of remedying the needs of less than fortunate children, parents, elderly, homeless veterans, and everyone else who deserves nutritional sustenance for the soul.
DEDICATION:
This script is dedicated to the memory of Nikolai Dmitriyevich Kondratiev (Никола́й Дми́триевич Кондра́тьев) as tribute for being a pioneering economist and statistician, paving the way for modern econometrics by advocation of rigorous and empirical methodologies. One of his most substantial contributions to the study of business cycle theory include a revolutionary hypothesis recognizing the existence of dynamic cycle-like phenomenon inherent to economies that are characterized by distinct phases of expansion, stagnation, recession and recovery, what we now know as "Kondratiev Waves" (K-waves). Kondratiev was one of the first economists to recognize the vital significance of applying quantitative analysis on empirical data to evaluate economic dynamics by means of statistical methods. His understanding was that conceptual models alone were insufficient to adequately interpret real-world economic conditions, and that sophisticated analysis was necessary to better comprehend the nature of trending/cycling economic behaviors. Additionally, he recognized prosperous economic cycles were predominantly driven by a combination of technological innovations and infrastructure investments that resulted in profound implications for economic growth and development.
I will mention this... nation's economies MUST be supported and defended to continuously evolve incrementally in order to flourish in perpetuity OR suffer through eras with lasting ramifications of societal stagnation and implosion.
Analogous to the realm of economics, aperiodic cycles/frequencies, both enduring and ephemeral, do exist in all facets of life, every second of every day. To name a few that any blind man can naturally see are: heartbeat (cardiac cycles), respiration rates, circadian rhythms of sleep, powerful magnetic solar cycles, seasonal cycles, lunar cycles, weather patterns, vegetative growth cycles, and ocean waves. Do not pretend for one second that these basic aforementioned examples do not affect business cycle fluctuations in minuscule and monumental ways hour to hour, day to day, season to season, year to year, and decade to decade in every nation on the planet. Kondratiev's original seminal theories in macroeconomics from nearly a century ago have proven remarkably prescient with many of his antiquated elementary observations/notions/hypotheses in macroeconomics being scholastically studied and topically researched further. Therefore, I am compelled to honor and recognize his statistical insight and foresight.
If only.. Kondratiev could hold a pocket sized computer in the cup of both hands bearing the TradingView logo and platform services, I truly believe he would be amazed in marvelous delight with a GARGANTUAN smile on his face.
INTRODUCTION:
Firstly, this is NOT technically speaking an indicator like most others. I would describe it as an advanced cycle period detector to obtain market data spectral estimates with low latency and moderate frequency resolution. Developers can take advantage of this detector by creating scripts that utilize a "Dominant Cycle Source" input to adaptively govern algorithms. Be forewarned, I would only recommend this for advanced developers, not novice code dabbling. Although, there is some Pine wizardry introduced here for novice Pine enthusiasts to witness and learn from. AI did describe the code into one super-crunched sentence as, "a rare feat of exceptionally formatted code masterfully balancing visual clarity, precision, and complexity to provide immense educational value for both programming newcomers and expert Pine coders alike."
Understand all of the above aforementioned? Buckle up and proceed for a lengthy read of verbose complexity...
This is my enhanced and heavily modified version of autocorrelation periodogram (ACP) for Pine Script v5.0. It was originally devised by the mathemagician John Ehlers for detecting dominant cycles (frequencies) in an asset's price action. I have been sitting on code similar to this for a long time, but I decided to unleash the advanced code with my fashion. Originally Ehlers released this with multiple versions, one in a 2016 TASC article and the other in his last published 2013 book "Cycle Analytics for Traders", chapter 8. He wasn't joking about "concepts of advanced technical trading" and ACP is nowhere near to his most intimidating and ingenious calculations in code. I will say the book goes into many finer details about the original periodogram, so if you wish to delve into even more elaborate info regarding Ehlers' original ACP form AND how you may adapt algorithms, you'll have to obtain one. Note to reader, comparing Ehlers' original code to my chimeric code embracing the "Power of Pine", you will notice they have little resemblance.
What you see is a new species of autocorrelation periodogram combining Ehlers' innovation with my fascinations of what ACP could be in a Pine package. One other intention of this script's code is to pay homage to Ehlers' lifelong works. Like Kondratiev, Ehlers is also a hardcore cycle enthusiast. I intend to carry on the fire Ehlers envisioned and I believe that is literally displayed here as a pleasant "fiery" example endowed with Pine. With that said, I tried to make the code as computationally efficient as possible, without going into dozens of more crazy lines of code to speed things up even more. There's also a few creative modifications I made by making alterations to the originating formulas that I felt were improvements, one of them being lag reduction. By recently questioning every single thing I thought I knew about ACP, combined with the accumulation of my current knowledge base, this is the innovative revision I came up with. I could have improved it more but decided not to mind thrash too many TV members, maybe later...
I am now confident Pine should have adequate overhead left over to attach various indicators to the dominant cycle via input.source(). TV, I apologize in advance if in the future a server cluster combusts into a raging inferno... Coders, be fully prepared to build entire algorithms from pure raw code, because not all of the built-in Pine functions fully support dynamic periods (e.g. length=ANYTHING). Many of them do, as this was requested and granted a while ago, but some functions are just inherently finicky due to implementation combinations and MUST be emulated via raw code. I would imagine some comprehensive library or numerous authored scripts have portions of raw code for Pine built-ins some where on TV if you look diligently enough.
Notice: Unfortunately, I will not provide any integration support into member's projects at all. I have my own projects that require way too much of my day already. While I was refactoring my life (forgoing many other "important" endeavors) in the early half of 2023, I primarily focused on this code over and over in my surplus time. During that same time I was working on other innovations that are far above and beyond what this code is. I hope you understand.
The best way programmatically may be to incorporate this code into your private Pine project directly, after brutal testing of course, but that may be too challenging for many in early development. Being able to see the periodogram is also beneficial, so input sourcing may be the "better" avenue to tether portions of the dominant cycle to algorithms. Unique indication being able to utilize the dominantCycle may be advantageous when tethering this script to those algorithms. The easiest way is to manually set your indicators to what ACP recognizes as the dominant cycle, but that's actually not considered dynamic real time adaption of an indicator. Different indicators may need a proportion of the dominantCycle, say half it's value, while others may need the full value of it. That's up to you to figure that out in practice. Sourcing one or more custom indicators dynamically to one detector's dominantCycle may require code like this: `int sourceDC = int(math.max(6, math.min(49, input.source(close, "Dominant Cycle Source"))))`. Keep in mind, some algos can use a float, while algos with a for loop require an integer.
I have witnessed a few attempts by talented TV members for a Pine based autocorrelation periodogram, but not in this caliber. Trust me, coding ACP is no ordinary task to accomplish in Pine and modifying it blessed with applicable improvements is even more challenging. For over 4 years, I have been slowly improving this code here and there randomly. It is beautiful just like a real flame, but... this one can still burn you! My mind was fried to charcoal black a few times wrestling with it in the distant past. My very first attempt at translating ACP was a month long endeavor because PSv3 simply didn't have arrays back then. Anyways, this is ACP with a newer engine, I hope you enjoy it. Any TV subscriber can utilize this code as they please. If you are capable of sufficiently using it properly, please use it wisely with intended good will. That is all I beg of you.
Lastly, you now see how I have rasterized my Pine with Ehlers' swami-like tech. Yep, this whole time I have been using hline() since PSv3, not plot(). Evidently, plot() still has a deficiency limited to only 32 plots when it comes to creating intense eye candy indicators, the last I checked. The use of hline() is the optimal choice for rasterizing Ehlers styled heatmaps. This does only contain two color schemes of the many I have formerly created, but that's all that is essentially needed for this gizmo. Anything else is generally for a spectacle or seeing how brutal Pine can be color treated. The real hurdle is being able to manipulate colors dynamically with Merlin like capabilities from multiple algo results. That's the true challenging part of these heatmap contraptions to obtain multi-colored "predator vision" level indication. You now have basic hline() food for thought empowerment to wield as you can imaginatively dream in Pine projects.
PERIODOGRAM UTILITY IN REAL WORLD SCENARIOS:
This code is a testament to the abilities that have yet to be fully realized with indication advancements. Periodograms, spectrograms, and heatmaps are a powerful tool with real-world applications in various fields such as financial markets, electrical engineering, astronomy, seismology, and neuro/medical applications. For instance, among these diverse fields, it may help traders and investors identify market cycles/periodicities in financial markets, support engineers in optimizing electrical or acoustic systems, aid astronomers in understanding celestial object attributes, assist seismologists with predicting earthquake risks, help medical researchers with neurological disorder identification, and detection of asymptomatic cardiovascular clotting in the vaxxed via full body thermography. In either field of study, technologies in likeness to periodograms may very well provide us with a better sliver of analysis beyond what was ever formerly invented. Periodograms can identify dominant cycles and frequency components in data, which may provide valuable insights and possibly provide better-informed decisions. By utilizing periodograms within aspects of market analytics, individuals and organizations can potentially refrain from making blinded decisions and leverage data-driven insights instead.
PERIODOGRAM INTERPRETATION:
The periodogram renders the power spectrum of a signal, with the y-axis representing the periodicity (frequencies/wavelengths) and the x-axis representing time. The y-axis is divided into periods, with each elevation representing a period. In this periodogram, the y-axis ranges from 6 at the very bottom to 49 at the top, with intermediate values in between, all indicating the power of the corresponding frequency component by color. The higher the position occurs on the y-axis, the longer the period or lower the frequency. The x-axis of the periodogram represents time and is divided into equal intervals, with each vertical column on the axis corresponding to the time interval when the signal was measured. The most recent values/colors are on the right side.
The intensity of the colors on the periodogram indicate the power level of the corresponding frequency or period. The fire color scheme is distinctly like the heat intensity from any casual flame witnessed in a small fire from a lighter, match, or camp fire. The most intense power would be indicated by the brightest of yellow, while the lowest power would be indicated by the darkest shade of red or just black. By analyzing the pattern of colors across different periods, one may gain insights into the dominant frequency components of the signal and visually identify recurring cycles/patterns of periodicity.
SETTINGS CONFIGURATIONS BRIEFLY EXPLAINED:
Source Options: These settings allow you to choose the data source for the analysis. Using the `Source` selection, you may tether to additional data streams (e.g. close, hlcc4, hl2), which also may include samples from any other indicator. For example, this could be my "Chirped Sine Wave Generator" script found in my member profile. By using the `SineWave` selection, you may analyze a theoretical sinusoidal wave with a user-defined period, something already incorporated into the code. The `SineWave` will be displayed over top of the periodogram.
Roofing Filter Options: These inputs control the range of the passband for ACP to analyze. Ehlers had two versions of his highpass filters for his releases, so I included an option for you to see the obvious difference when performing a comparison of both. You may choose between 1st and 2nd order high-pass filters.
Spectral Controls: These settings control the core functionality of the spectral analysis results. You can adjust the autocorrelation lag, adjust the level of smoothing for Fourier coefficients, and control the contrast/behavior of the heatmap displaying the power spectra. I provided two color schemes by checking or unchecking a checkbox.
Dominant Cycle Options: These settings allow you to customize the various types of dominant cycle values. You can choose between floating-point and integer values, and select the rounding method used to derive the final dominantCycle values. Also, you may control the level of smoothing applied to the dominant cycle values.
DOMINANT CYCLE VALUE SELECTIONS:
External to the acs() function, the code takes a dominant cycle value returned from acs() and changes its numeric form based on a specified type and form chosen within the indicator settings. The dominant cycle value can be represented as an integer or a decimal number, depending on the attached algorithm's requirements. For example, FIR filters will require an integer while many IIR filters can use a float. The float forms can be either rounded, smoothed, or floored. If the resulting value is desired to be an integer, it can be rounded up/down or just be in an integer form, depending on how your algorithm may utilize it.
AUTOCORRELATION SPECTRUM FUNCTION BASICALLY EXPLAINED:
In the beginning of the acs() code, the population of caches for precalculated angular frequency factors and smoothing coefficients occur. By precalculating these factors/coefs only once and then storing them in an array, the indicator can save time and computational resources when performing subsequent calculations that require them later.
In the following code block, the "Calculate AutoCorrelations" is calculated for each period within the passband width. The calculation involves numerous summations of values extracted from the roofing filter. Finally, a correlation values array is populated with the resulting values, which are normalized correlation coefficients.
Moving on to the next block of code, labeled "Decompose Fourier Components", Fourier decomposition is performed on the autocorrelation coefficients. It iterates this time through the applicable period range of 6 to 49, calculating the real and imaginary parts of the Fourier components. Frequencies 6 to 49 are the primary focus of interest for this periodogram. Using the precalculated angular frequency factors, the resulting real and imaginary parts are then utilized to calculate the spectral Fourier components, which are stored in an array for later use.
The next section of code smooths the noise ridden Fourier components between the periods of 6 and 49 with a selected filter. This species also employs numerous SuperSmoothers to condition noisy Fourier components. One of the big differences is Ehlers' versions used basic EMAs in this section of code. I decided to add SuperSmoothers.
The final sections of the acs() code determines the peak power component for normalization and then computes the dominant cycle period from the smoothed Fourier components. It first identifies a single spectral component with the highest power value and then assigns it as the peak power. Next, it normalizes the spectral components using the peak power value as a denominator. It then calculates the average dominant cycle period from the normalized spectral components using Ehlers' "Center of Gravity" calculation. Finally, the function returns the dominant cycle period along with the normalized spectral components for later external use to plot the periodogram.
POST SCRIPT:
Concluding, I have to acknowledge a newly found analyst for assistance that I couldn't receive from anywhere else. For one, Claude doesn't know much about Pine, is unfortunately color blind, and can't even see the Pine reference, but it was able to intuitively shred my code with laser precise realizations. Not only that, formulating and reformulating my description needed crucial finesse applied to it, and I couldn't have provided what you have read here without that artificial insight. Finding the right order of words to convey the complexity of ACP and the elaborate accompanying content was a daunting task. No code in my life has ever absorbed so much time and hard fricking work, than what you witness here, an ACP gem cut pristinely. I'm unveiling my version of ACP for an empowering cause, in the hopes a future global army of code wielders will tether it to highly functional computational contraptions they might possess. Here is ACP fully blessed poetically with the "Power of Pine" in sublime code. ENJOY!
Autocorrelation - The Quant ScienceAutocorrelation - The Quant Science it is an indicator developed to quickly calculate the autocorrelation of a historical series. The objective of this indicator is to plot the autocorrelation values and highlight market moments where the value is positive and exceeds the attention threshold.
This indicator can be used for manual analysis when a trader needs to search for new price patterns within the historical series or to create complex formulas in estimating future prices.
What is autocorrelation?
Autocorrelation in trading is a statistical measure used to determine the presence of a relationship or pattern of dependence between values in a financial time series over time. It represents the correlation of past values in a series with its future values. In other words, autocorrelation in trading aims to identify if there are systematic relationships between the past prices or returns of a security or market and its future prices or returns. This analysis can be helpful in identifying patterns or trends that can be leveraged for informed trading decisions. The presence of autocorrelation may suggest that market prices or returns follow a certain pattern or trend over time.
Limitations of the model
It is important to note that autocorrelation does not necessarily imply a causal relationship between past and future values. Other variables or market factors may influence the dynamics of prices or returns, and therefore autocorrelation could be merely a random coincidence. Therefore, it is essential to carefully evaluate the results of autocorrelation analysis along with other information and trading strategies to make informed decisions.
How to use
The usage is very simple, you just need to add it to the current chart to activate the indicator.
From the user interface, you can manage two important features:
1. Lenght: the delay period applied to the historical series during the autocorrelation calculation can be managed from the user interface. By default, it is set to 20, which means that the autocorrelation ratio within the historical series is calculated with a delay of 20 bars.
2. Threshold: the threshold value that the autocorrelation level must meet can be managed from the user interface. By default, it is set to 0.50, which means that the autocorrelation value must be higher than this threshold to be considered valid and displayed on the chart.
3. Bar color: the color used to display the autocorrelation data and highlight the bars when autocorrelation is valid can be managed from the user interface.
To set up the chart
We recommend disabling the 'wick' and 'border' of the candlesticks from the chart settings for a high-quality user experience.
8 Day Run - Momentum StrategyInspired by Linda Bradford Raschke.
Entry criteria:
This strategy is used to capture momentum effects on the daily periodicities. Once prices have had a run of 8 or more consecutive closes above or below the 5-period simple moving average the strategy is primed to trade.
It will then enter a short on the first close above the 5sma after a run of 8 or more closes below the 5sma (it will enter a long when the price closes below the 5sma after a run of 8 or more closes above the 5sma).
Exit criteria:
All trades are exited on the first close back above/ below the 5sma.
Levinson-Durbin Autocorrelation Extrapolation of Price [Loxx]Levinson-Durbin Autocorrelation Extrapolation of Price is an indicator that uses the Levinson recursion or Levinson–Durbin recursion algorithm to predict price moves. This method is commonly used in speech modeling and prediction engines.
What is Levinson recursion or Levinson–Durbin recursion?
Is a linear algebra prediction analysis that is performed once per bar using the autocorrelation method with a within a specified asymmetric window. The autocorrelation coefficients of the window are computed and converted to LP coefficients using the Levinson algorithm. The LP coefficients are then transformed to line spectrum pairs for quantization and interpolation. The interpolated quantized and unquantized filters are converted back to the LP filter coefficients to construct the synthesis and weighting filters for each bar.
Data inputs
Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar
LastBar - bar where to start the prediction
PastBars - how many bars back to model
LPOrder - order of linear prediction model; 0 to 1
FutBars - how many bars you want to forward predict
Things to know
Normally, a simple moving average is caculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages.
This indicator repaints
Included
Bar color muting
Further reading
Implementing the Levinson-Durbin Algorithm on the StarCore™ SC140/SC1400 Cores
LevinsonDurbin_G729 Algorithm, Calculates LP coefficients from the autocorrelation coefficients. Intel® Integrated Performance Primitives for Intel® Architecture Reference Manual
APA-Adaptive, Ehlers Early Onset Trend [Loxx]APA-Adaptive, Ehlers Early Onset Trend is Ehlers Early Onset Trend but with Autocorrelation Periodogram Algorithm dominant cycle period input.
What is Ehlers Early Onset Trend?
The Onset Trend Detector study is a trend analyzing technical indicator developed by John F. Ehlers , based on a non-linear quotient transform. Two of Mr. Ehlers' previous studies, the Super Smoother Filter and the Roofing Filter, were used and expanded to create this new complex technical indicator. Being a trend-following analysis technique, its main purpose is to address the problem of lag that is common among moving average type indicators.
The Onset Trend Detector first applies the EhlersRoofingFilter to the input data in order to eliminate cyclic components with periods longer than, for example, 100 bars (default value, customizable via input parameters) as those are considered spectral dilation. Filtered data is then subjected to re-filtering by the Super Smoother Filter so that the noise (cyclic components with low length) is reduced to minimum. The period of 10 bars is a default maximum value for a wave cycle to be considered noise; it can be customized via input parameters as well. Once the data is cleared of both noise and spectral dilation, the filter processes it with the automatic gain control algorithm which is widely used in digital signal processing. This algorithm registers the most recent peak value and normalizes it; the normalized value slowly decays until the next peak swing. The ratio of previously filtered value to the corresponding peak value is then quotiently transformed to provide the resulting oscillator. The quotient transform is controlled by the K coefficient: its allowed values are in the range from -1 to +1. K values close to 1 leave the ratio almost untouched, those close to -1 will translate it to around the additive inverse, and those close to zero will collapse small values of the ratio while keeping the higher values high.
Indicator values around 1 signify uptrend and those around -1, downtrend.
What is an adaptive cycle, and what is Ehlers Autocorrelation Periodogram Algorithm?
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers , 2013, page 135:
"Adaptive filters can have several different meanings. For example, Perry Kaufman’s adaptive moving average ( KAMA ) and Tushar Chande’s variable index dynamic average ( VIDYA ) adapt to changes in volatility . By definition, these filters are reactive to price changes, and therefore they close the barn door after the horse is gone.The adaptive filters discussed in this chapter are the familiar Stochastic , relative strength index ( RSI ), commodity channel index ( CCI ), and band-pass filter.The key parameter in each case is the look-back period used to calculate the indicator. This look-back period is commonly a fixed value. However, since the measured cycle period is changing, it makes sense to adapt these indicators to the measured cycle period. When tradable market cycles are observed, they tend to persist for a short while.Therefore, by tuning the indicators to the measure cycle period they are optimized for current conditions and can even have predictive characteristics.
The dominant cycle period is measured using the Autocorrelation Periodogram Algorithm. That dominant cycle dynamically sets the look-back period for the indicators. I employ my own streamlined computation for the indicators that provide smoother and easier to interpret outputs than traditional methods. Further, the indicator codes have been modified to remove the effects of spectral dilation.This basically creates a whole new set of indicators for your trading arsenal."
Ehlers Autocorrelation Periodogram [Loxx]Ehlers Autocorrelation Periodogram contains two versions of Ehlers Autocorrelation Periodogram Algorithm. This indicator is meant to supplement adaptive cycle indicators that myself and others have published on Trading View, will continue to publish on Trading View. These are fast-loading, low-overhead, streamlined, exact replicas of Ehlers' work without any other adjustments or inputs.
Versions:
- 2013, Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers
- 2016, TASC September, "Measuring Market Cycles"
Description
The Ehlers Autocorrelation study is a technical indicator used in the calculation of John F. Ehlers’s Autocorrelation Periodogram. Its main purpose is to eliminate noise from the price data, reduce effects of the “spectral dilation” phenomenon, and reveal dominant cycle periods. The spectral dilation has been discussed in several studies by John F. Ehlers; for more information on this, refer to sources in the "Further Reading" section.
As the first step, Autocorrelation uses Mr. Ehlers’s previous installment, Ehlers Roofing Filter, in order to enhance the signal-to-noise ratio and neutralize the spectral dilation. This filter is based on aerospace analog filters and when applied to market data, it attempts to only pass spectral components whose periods are between 10 and 48 bars.
Autocorrelation is then applied to the filtered data: as its name implies, this function correlates the data with itself a certain period back. As with other correlation techniques, the value of +1 would signify the perfect correlation and -1, the perfect anti-correlation.
Using values of Autocorrelation in Thermo Mode may help you reveal the cycle periods within which the data is best correlated (or anti-correlated) with itself. Those periods are displayed in the extreme colors (orange) while areas of intermediate colors mark periods of less useful cycles.
What is an adaptive cycle, and what is the Autocorrelation Periodogram Algorithm?
From his Ehlers' book mentioned above, page 135:
"Adaptive filters can have several different meanings. For example, Perry Kaufman’s adaptive moving average ( KAMA ) and Tushar Chande’s variable index dynamic average ( VIDYA ) adapt to changes in volatility . By definition, these filters are reactive to price changes, and therefore they close the barn door after the horse is gone.The adaptive filters discussed in this chapter are the familiar Stochastic , relative strength index ( RSI ), commodity channel index ( CCI ), and band-pass filter.The key parameter in each case is the look-back period used to calculate the indicator.This look-back period is commonly a fixed value. However, since the measured cycle period is changing, as we have seen in previous chapters, it makes sense to adapt these indicators to the measured cycle period. When tradable market cycles are observed, they tend to persist for a short while.Therefore, by tuning the indicators to the measure cycle period they are optimized for current conditions and can even have predictive characteristics.
The dominant cycle period is measured using the Autocorrelation Periodogram Algorithm. That dominant cycle dynamically sets the look-back period for the indicators. I employ my own streamlined computation for the indicators that provide smoother and easier to interpret outputs than traditional methods. Further, the indicator codes have been modified to remove the effects of spectral dilation.This basically creates a whole new set of indicators for your trading arsenal."
How to use this indicator
The point of the Ehlers Autocorrelation Periodogram Algorithm is to dynamically set a period between a minimum and a maximum period length. While I leave the exact explanation of the mechanic to Dr. Ehlers’s book, for all practical intents and purposes, in my opinion, the punchline of this method is to attempt to remove a massive source of overfitting from trading system creation–namely specifying a look-back period. SMA of 50 days? 100 days? 200 days? Well, theoretically, this algorithm takes that possibility of overfitting out of your hands. Simply, specify an upper and lower bound for your look-back, and it does the rest. In addition, this indicator tells you when its best to use adaptive cycle inputs for your other indicators.
Usage Example 1
Let's say you're using "Adaptive Qualitative Quantitative Estimation (QQE) ". This indicator has the option of adaptive cycle inputs. When the "Ehlers Autocorrelation Periodogram " shows a period of high correlation that adaptive cycle inputs work best during that period.
Usage Example 2
Check where the dominant cycle line lines, grab that output number and inject it into your other standard indicators for the length input.
Ehlers Adaptive Relative Strength Index (RSI) [Loxx]Ehlers Adaptive Relative Strength Index (RSI) is an implementation of RSI using Ehlers Autocorrelation Periodogram Algorithm to derive the length input for RSI. Other implementations of Ehers Adaptive RSI rely on the inferior Hilbert Transformer derive the dominant cycle.
In his book "Cycle Analytics for Traders Advanced Technical Trading Concepts", John F. Ehlers describes an implementation for Adaptive Relative Strength Index in order to solve for varying length inputs into the classic RSI equation.
What is an adaptive cycle, and what is the Autocorrelation Periodogram Algorithm?
From his Ehlers' book mentioned above, page 135:
"Adaptive filters can have several different meanings. For example, Perry Kaufman’s adaptive moving average (KAMA) and Tushar Chande’s variable index dynamic average (VIDYA) adapt to changes in volatility. By definition, these filters are reactive to price changes, and therefore they close the barn door after the horse is gone.The adaptive filters discussed in this chapter are the familiar Stochastic, relative strength index (RSI), commodity channel index (CCI), and band-pass filter.The key parameter in each case is the look-back period used to calculate the indicator.This look-back period is commonly a fixed value. However, since the measured cycle period is changing, as we have seen in previous chapters, it makes sense to adapt these indicators to the measured cycle period. When tradable market cycles are observed, they tend to persist for a short while.Therefore, by tuning the indicators to the measure cycle period they are optimized for current conditions and can even have predictive characteristics.
The dominant cycle period is measured using the autocorrelation periodogram algorithm. That dominant cycle dynamically sets the look-back period for the indicators. I employ my own streamlined computation for the indicators that provide smoother and easier to interpret outputs than traditional methods. Further, the indicator codes have been modified to remove the effects of spectral dilation.This basically creates a whole new set of indicators for your trading arsenal."
What is Adaptive RSI?
From his Ehlers' book mentioned above, page 137:
"The adaptive RSI starts with the computation of the dominant cycle using the autocorrelation periodogram approach. Since the objective is to use only those frequency components passed by the roofing filter, the variable "filt" is used as a data input rather than closing prices. Rather than independently taking the averages of the numerator and denominator, I chose to perform smoothing on the ratio using the SuperSmoother filter. The coefficients for the SuperSmoother filters have previously been computed in the dominant cycle measurement part of the code."
Happy trading!
Adaptive Average Vortex Index [lastguru]As a longtime fan of ADX, looking at Vortex Indicator I often wondered, where is the third line. I have rarely seen that anybody is calculating it. So, here it is: Average Vortex Index - an ADX calculated from Vortex Indicator. I interpret it similarly to the ADX indicator: higher values show stronger trend. If you discover other interpretation or have suggestions, comments are welcome.
Both VI+ and VI- lines are also drawn. As I use adaptive length calculation in my other scripts (based on the libraries I've developed and published), I have also included the possibility to have an adaptive length here, so if you hate the idea of calculating ADX from VI, you can disable that line and just look at the adaptive Vortex Indicator.
Note that as with all my oscillators, all the lines here are renormalized to -1..1 range unlike the original Vortex Indicator computation. To do that for VI+ and VI- lines, I subtract 1 from their values. It does not change the shape or the amplitude of the lines.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers . I do not know, which combination works best, so you can experiment.
If no Adaptation is selected ( None option), you can set Length directly. If an Adaptation is selected, then Cycle multiplier can be set.
The oscillator also has the option to configure the internal smoothing function with Window setting. By default, RMA is used (like in ADX calculation). Fast Default option is using half the length for smoothing. Triangle , Hamming and Hann Window algorithms are some better smoothers suggested by John F. Ehlers.
After the oscillator a Moving Average can be applied. The following Moving Averages are included: SMA , RMA, EMA , HMA , VWMA , 2-pole Super Smoother, 3-pole Super Smoother, Filt11, Triangle Window, Hamming Window, Hann Window, Lowpass, DSSS.
Postfilter options are applied last:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic ) by John F. Ehlers
Inverse Fisher Transform - Inverse Fisher Transform
Noise Elimination Technology - a simplified Kendall correlation algorithm "Noise Elimination Technology" by John F. Ehlers
Momentum - momentum (derivative)
Except for Inverse Fisher Transform , all Postfilter algorithms can have Length parameter. If it is not specified (set to 0), then the calculated Slow MA Length is used. If Filter/MA Length is less than 2 or Postfilter Length is less than 1, they are calculated as a multiplier of the calculated oscillator length.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.
Adaptive MA Difference constructor [lastguru]A complimentary indicator to my Adaptive MA constructor. It calculates the difference between the two MA lines (inspired by the Moving Average Difference (MAD) indicator by John F. Ehlers). You can then further smooth the resulting curve. The parameters and options are explained here:
The difference is normalized by dividing the difference by twice its Root mean square (RMS) over Slow MA length. Inverse Fisher Transform is then used to force the -1..1 range.
Same Postfilter options are provided as in my Adaptive Oscillator constructor:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic ) by John F. Ehlers
Inverse Fisher Transform - Inverse Fisher Transform
Noise Elimination Technology - a simplified Kendall correlation algorithm "Noise Elimination Technology" by John F. Ehlers
Momentum - momentum (derivative)
Except for Inverse Fisher Transform, all Postfilter algorithms can have Length parameter. If it is not specified (set to 0), then the calculated Slow MA Length is used.
Adaptive MA constructor [lastguru]Adaptive Moving Averages are nothing new, however most of them use EMA as their MA of choice once the preferred smoothing length is determined. I have decided to make an experiment and separate length generation from smoothing, offering multiple alternatives to be combined. Some of the combinations are widely known, some are not. This indicator is based on my previously published public libraries and also serve as a usage demonstration for them. I will try to expand the collection (suggestions are welcome), however it is not meant as an encyclopaedic resource, so you are encouraged to experiment yourself: by looking on the source code of this indicator, I am sure you will see how trivial it is to use the provided libraries and expand them with your own ideas and combinations. I give no recommendation on what settings to use, but if you find some useful setting, combination or application ideas (or bugs in my code), I would be happy to read about them in the comments section.
The indicator works in three stages: Prefiltering, Length Adaptation and Moving Averages.
Prefiltering is a fast smoothing to get rid of high-frequency (2, 3 or 4 bar) noise.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
Chande (Price) - based on Chande's Dynamic Momentum Index (CDMI or DYMOI), which is dynamic RSI with this length
Chande (Volume) - a variant of Chande's algorithm, where volume is used instead of price
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Deviation Scaling - based on DSSS by John F. Ehlers
Median Average - based on Median Average Adaptive Filter by John F. Ehlers
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Alpha - based on MESA Adaptive Moving Average by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers, but unlike Alpha calculation, this adaptation estimates cycle period
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers. I do not know, which combination works best, so you can experiment.
Chande's Adaptations also have 3 additional parameters: SD Length (lookback length of Standard deviation), Smooth (smoothing length of Standard deviation) and Power (exponent of the length adaptation - lower is smaller variation). These are internal tweaks for the calculation.
Length Adaptaton section offer you a choice of Moving Average algorithms. Most of the Adaptations are originally used with EMA, so this is a good starting point for exploration.
SMA - Simple Moving Average
RMA - Running Moving Average
EMA - Exponential Moving Average
HMA - Hull Moving Average
VWMA - Volume Weighted Moving Average
2-pole Super Smoother - 2-pole Super Smoother by John F. Ehlers
3-pole Super Smoother - 3-pole Super Smoother by John F. Ehlers
Filt11 -a variant of 2-pole Super Smoother with error averaging for zero-lag response by John F. Ehlers
Triangle Window - Triangle Window Filter by John F. Ehlers
Hamming Window - Hamming Window Filter by John F. Ehlers
Hann Window - Hann Window Filter by John F. Ehlers
Lowpass - removes cyclic components shorter than length (Price - Highpass)
DSSS - Derivation Scaled Super Smoother by John F. Ehlers
There are two Moving Averages that are drown on the chart, so length for both needs to be selected. If no Adaptation is selected ( None option), you can set Fast Length and Slow Length directly. If an Adaptation is selected, then Cycle multiplier can be selected for Fast and Slow MA.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.
DominantCycleCollection of Dominant Cycle estimators. Length adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly). This collection may become encyclopaedic, so if you have any working cycle estimator, drop me a line in the comments below. Suggestions are welcome. Currently included estimators are based on the work of John F. Ehlers
mamaPeriod(src, dynLow, dynHigh) MESA Adaptation - MAMA Cycle
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on MESA Adaptive Moving Average by John F. Ehlers
Performs Hilbert Transform Homodyne Discriminator cycle measurement
Unlike MAMA Alpha function (in LengthAdaptation library), this does not compute phase rate of change
Introduced in the September 2001 issue of Stocks and Commodities
Inspired by the @everget implementation:
Inspired by the @anoojpatel implementation:
paPeriod(src, dynLow, dynHigh, preHP, preSS, preHP) Pearson Autocorrelation
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter (default)
preSS : Use Super Smoother prefilter (default)
preHP : Use Hann Windowing prefilter
Returns: Calculated period
Based on Pearson Autocorrelation Periodogram by John F. Ehlers
Introduced in the September 2016 issue of Stocks and Commodities
Inspired by the @blackcat1402 implementation:
Inspired by the @rumpypumpydumpy implementation:
Corrected many errors, and made small speed optimizations, so this could be the best implementation to date (still slow, though, so may revisit in future)
High Pass and Super Smoother prefilters are used in the original implementation
dftPeriod(src, dynLow, dynHigh, preHP, preSS, preHP) Discrete Fourier Transform
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter (default)
preSS : Use Super Smoother prefilter (default)
preHP : Use Hann Windowing prefilter
Returns: Calculated period
Based on Spectrum from Discrete Fourier Transform by John F. Ehlers
Inspired by the @blackcat1402 implementation:
High Pass, Super Smoother and Hann Windowing prefilters are used in the original implementation
phasePeriod(src, dynLow, dynHigh, preHP, preSS, preHP) Phase Accumulation
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter (default)
preSS : Use Super Smoother prefilter (default)
preHP : Use Hamm Windowing prefilter
Returns: Calculated period
Based on Dominant Cycle from Phase Accumulation by John F. Ehlers
High Pass and Super Smoother prefilters are used in the original implementation
doAdapt(type, src, len, dynLow, dynHigh, chandeSDLen, chandeSmooth, chandePower, preHP, preSS, preHP) Execute a particular Length Adaptation or Dominant Cycle Estimator from the list
Parameters:
type : Length Adaptation or Dominant Cycle Estimator type to use
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
chandeSDLen : Lookback length of Standard deviation for Chande's Dynamic Length
chandeSmooth : Smoothing length of Standard deviation for Chande's Dynamic Length
chandePower : Exponent of the length adaptation for Chande's Dynamic Length (lower is smaller variation)
preHP : Use High Pass prefilter for the Estimators that support it (default)
preSS : Use Super Smoother prefilter for the Estimators that support it (default)
preHP : Use Hann Windowing prefilter for the Estimators that support it
Returns: Calculated period (float, not limited)
doEstimate(type, src, dynLow, dynHigh, preHP, preSS, preHP) Execute a particular Dominant Cycle Estimator from the list
Parameters:
type : Dominant Cycle Estimator type to use
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter for the Estimators that support it (default)
preSS : Use Super Smoother prefilter for the Estimators that support it (default)
preHP : Use Hann Windowing prefilter for the Estimators that support it
Returns: Calculated period (float, not limited)
Adaptive Trend Cipher loxx]Adaptive Trend Cipher
Highly experimental!
Features:
-Implements 5 different Dominant Adaptive Cycle Measures to determine optimal inputs for correlation functions. These cycle calculations include the following: **
* Ehler's Autocorrelation Dominant Cycle
* Ehler's Instantaneous Dominant Cycle
* Ehler's Band-pass Dominant Cycle
* Ehler's Hilbert Period Dominant Cycle
* Ehler's Dual Differentiator Dominant Cycle
**additional cycle measures to be added in future releases
-Uses price to time correlation with look-back periods determined by the dominant cycle measures
-Allows users to manipulate the range of Dominant Cycle inputs, also allows the user to change the size % of the the output Dominant cycle to be used to determine correlation lengths
-Bars are colored according to correlation extremes. Green bars are uptrend, Red bars are downtrend; Yellow bars are high correlation, Fuchsia bars are low correlation
Uses
-Trend cipher is a novel approach to teasing out macro trends in the market. This version is geared to be used on the daily time frame only
-Reversals at yellow and fuchsia bars when they appear, it shows price exhaustion using
Warning: This may not work on certain assets due to the high processing power required to calculate cycle dominance. This also uses a custom correlation function since the data being input intot he correlation function is not constant but variable based on cycle dominance at every bar. To correct this in most circumstances you must change the max_bars_back constant in the indicator method call
If you use parts of the code, please let me know, I would love to hear what you do with it.
Happy trading!
conditional_returnsThis script attempts to contextualize the instrument's latest return. It asks, "when a return of the same or greater magnitude occurred in the past, in the same direction, what was the following period's return?"
By default, the latest return is used. For example, on a daily chart, that would mean "today's" return. However, you can select any return you want using the "override" input.
The output table shows:
- The latest/override return, as a percentage. This is in the top left, fuchsia cell.
The first three, blue columns, show:
- The count of up and down (or positive and negative) next period returns. This shows you the sample size.
- The percentage of up/down next period returns.
- The average next-period return return, up and down, as percentages.
The next three, green columns show these same statistics, but for all returns--every period in the active date range is used. This data serves as a basis for comparison.
Note that you can select a custom date range with the "start" and "end" inputs. The corresponding area on the chart is shaded light grey, to show which data is used in the computations.
Ehlers AutoCorrelation Indicator [CC]The AutoCorrelation Indicator was created by John Ehlers (Cycle Analytics pgs 94-98) and this can be viewed as both a momentum indicator and a trend indicator. This was his basis for several other indicators that he created which I will be publishing soon but essentially as this indicator goes up then the stock is in an uptrend and also has upward momentum. You will notice that this indicator starts to go down even during an uptrend showing that the underlying trend is going to have an upcoming reversal. He also warns that the halfway mark is a possible reversal point so keep an eye out for that.
Generally speaking a good signal is to enter a long position when the indicator is under the midline and is starting to go up (or when the line is green) and to exit the position when the indicator goes over the midline. I have included strong buy and sell signals in addition to normal ones so darker colors mean strong signals and lighter colors mean normal signals.
Let me know if there are any other indicators you would like me to publish!
Test - Gramian Angular FieldExperimental:
The Gramian Angular Field is usually used in machine learning for machine vision, it allows the encoding of data as a visual queue / matrix.
Auto_Corr_DailyThis indicator shows the Pearson correlation coefficient between different periods of one financial instrument. Two dates are set, which are the starting points of two series, between which the correlation coefficient is calculated. The correlation period is taken from the difference of the current date from the second reference point. The indicator is designed to analyze the correlation only on the 1D timeframe.
[blackcat] L2 Ehlers Adaptive Jon Andersen R-Squared IndicatorLevel: 2
Background
@pips_v1 has proposed an interesting idea that is it possible to code an "Adaptive Jon Andersen R-Squared Indicator" where the length is determined by DCPeriod as calculated in Ehlers Sine Wave Indicator? I agree with him and starting to construct this indicator. After a study, I found "(blackcat) L2 Ehlers Autocorrelation Periodogram" script could be reused for this purpose because Ehlers Autocorrelation Periodogram is an ideal candidate to calculate the dominant cycle. On the other hand, there are two inputs for R-Squared indicator:
Length - number of bars to calculate moment correlation coefficient R
AvgLen - number of bars to calculate average R-square
I used Ehlers Autocorrelation Periodogram to produced a dynamic value of "Length" of R-Squared indicator and make it adaptive.
Function
One tool available in forecasting the trendiness of the breakout is the coefficient of determination (R-squared), a statistical measurement. The R-squared indicates linear strength between the security's price (the Y - axis) and time (the X - axis). The R-squared is the percentage of squared error that the linear regression can eliminate if it were used as the predictor instead of the mean value. If the R-squared were 0.99, then the linear regression would eliminate 99% of the error for prediction versus predicting closing prices using a simple moving average.
When the R-squared is at an extreme low, indicating that the mean is a better predictor than regression, it can only increase, indicating that the regression is becoming a better predictor than the mean. The opposite is true for extreme high values of the R-squared.
To make this indicator adaptive, the dominant cycle is extracted from the spectral estimate in the next block of code using a center-of-gravity ( CG ) algorithm. The CG algorithm measures the average center of two-dimensional objects. The algorithm computes the average period at which the powers are centered. That is the dominant cycle. The dominant cycle is a value that varies with time. The spectrum values vary between 0 and 1 after being normalized. These values are converted to colors. When the spectrum is greater than 0.5, the colors combine red and yellow, with yellow being the result when spectrum = 1 and red being the result when the spectrum = 0.5. When the spectrum is less than 0.5, the red saturation is decreased, with the result the color is black when spectrum = 0.
Construction of the autocorrelation periodogram starts with the autocorrelation function using the minimum three bars of averaging. The cyclic information is extracted using a discrete Fourier transform (DFT) of the autocorrelation results. This approach has at least four distinct advantages over other spectral estimation techniques. These are:
1. Rapid response. The spectral estimates start to form within a half-cycle period of their initiation.
2. Relative cyclic power as a function of time is estimated. The autocorrelation at all cycle periods can be low if there are no cycles present, for example, during a trend. Previous works treated the maximum cycle amplitude at each time bar equally.
3. The autocorrelation is constrained to be between minus one and plus one regardless of the period of the measured cycle period. This obviates the need to compensate for Spectral Dilation of the cycle amplitude as a function of the cycle period.
4. The resolution of the cyclic measurement is inherently high and is independent of any windowing function of the price data.
Key Signal
DC --> Ehlers dominant cycle.
AvgSqrR --> R-squared output of the indicator.
Remarks
This is a Level 2 free and open source indicator.
Feedbacks are appreciated.
test - autocorrelation distributionexperimental:
shows the distribution for each shift in a autocorrelation.
