Prometheus Analytics Hurst ExponentThis indicator uses market data to calculate the Hurst Exponent so traders can have knowledge of the long memory of the asset.
Users can control the lookback length for the H value (Hurst Exponent), lookback length for the SMA (Simple Moving Average) of the Hurst Exponent, to show either, and what to calculate the H value and SMA on.
Hurst Exponent:
The Hurst Exponent is a value between 0 and 1 with 0.5 as a midline.
An H value(Hurst Exponent) above 0.5 indicates a trending market, and a market that should have larger, longer moves.
An H value below 0.5 indicates a mean reverting market, and a market that should have smaller, shorter moves.
An H value of0.5 indicates a random walk. This would mean the price would follow a Brownian Motion model and future prices would be independent from past prices.
Just because the H value is above 0.5 does not indicate that there should be an UP trend, just as a value below 0.5 does not indicate a DOWN trend. It indicates that there should be a trend, up or down.
Scenarios:
An intuitive way to use the Hurst Exponent is as an asset is trending in whatever direction, as the H value crosses below 0.5 it indicates a reversal. It indicates that what was happening before isn’t impacting what is happening now as much.
Steps explained from picture:
Step 1: Strong uptrend is identified with the asset moving up aggressively with H above 0.5.
Step 2: The H value crosses below 0.5 and prices stay elevated.
Step 3: Price reverts back down as the H value stays below 0.5
Just because the H value is above 0.5 doesn’t mean the asset has to be uptrending. In this example we see the asset fall as the H value is above 0.5. Not only that, but every time it crosses below 0.5, the asset takes a breather on the way down
Step 1: As the H value crosses above 0.5, we can expect trends to appear in the asset.
Step 2: After the trend switches to down, we only see a breather and some chop after the H value crosses back below 0.5.
Step 3: Once The H value crosses back over we see the downtrend continue and new lows be made.
Step 4: We see it once again, simply the area of chop is bigger. We don’t see a higher high, breaking the overall downtrend, but once the H value crosses over again the downturn continues and we see a lower low.
It may occur when no strong trend is made in either direction. The H value above 0.5 does indeed sometimes correlate with an uptrend sometimes.
Step 1: After the strong downtrend we see a break below 0.5 with some consolidation.
Step 2: No clear big move on the asset or H value.
Step 3: H value above 0.5 leads to a break of highs and a new uptrend.
Users have the option to decide what to calculate the H value on. Close is the default, or dollar return per bar are the options. Dollar return per bar and offer an H value that may give a better indication of when price moves will be small and sporadic.
Using dollar move per bar.
Step 1: H value cross above 0.5, we see large candles and fast moves.
Step 2: H value crosses below 0.5, the candles immediately following are shorter. The big red candles come right before the cross back above.
Step 3: H value cross back above 0.5, after some chop, large move down.
Similar story
Step 1: H value above 0.5, big trends either direction
Step 2: After the H value crosses below, the moves are short and choppy.
Settings:
Options to show or remove either the H value or it’s SMA.
Options to adjust the period uses, default is (32, 16)
在腳本中搜尋"hurst"
Dominant Cycle Detection OscillatorThis is a Dominant Cycle Detection Oscillator that searches multiple ranges of wavelengths within a spectrum. Choose one of 4 different dominant cycle detection methods (MESA MAMA cycle, Pearson Autocorrelation, Discreet Fourier Transform, and Phase Accumulation) to determine the most dominant cycles and see the historical results. Straight lines can indicate a steady dominant cycle; while Wavy lines might indicate a varying dominant cycle length. The steadier the cycle, the easier it may be to predict future events in that cycle (keep the log scale in mind when considering steadiness). The presence of evenly divisible (or harmonic) cycle lengths may also indicate stronger cycles; for example, 19, 38, and 76 dominant lengths for the 2x, 4x, and 8x cycles. Practically, a trader can use these cycle outputs as the default settings for other Hurst/cycle indicators. For example, if you see dominant cycle oscillator outputs of 38 & 76 for the 4x and 8x cycle respectively, you might want to test/use defaults of 38 & 76 for the 4x & 8x lengths in the bandpass, diamond/semi-circle notation, moving average & envelope, and FLD instead of the defaults 40 & 80 for a more fine-tuned analysis.
Muting the oscillator's historical lines and overlaying the indicator on the chart can visually cue a trader to the cycle lengths without taking up extra panes. The DFT Cycle lengths with muted historical lines have been overlayed on the chart in the photo.
The y-axis scale for this indicator's pane (just the oscillator pane, not the chart) most likely needs to be changed to logarithmic to look normal, but it depends on the search ranges in your settings. There are instructions in the settings. In the photo, the MESA MAMA scale is set to regular (not logarithmic) which demonstrates how difficult it can be to read if not changed.
In the Spectral Analysis chapter of Hurst's book Profit Magic, he recommended doing a Fourier analysis across a spectrum of frequencies. Hurst acknowledged there were many ways to do this analysis but recommended the method described by Lanczos. Currently in this indicator, the closest thing to the method described by Lanczos is the DFT Discreet Fourier Transform method.
Shoutout to @lastguru for the dominant cycle library referenced in this code. He mentioned that he may add more methods in the future.
SemiCircle Cycle Notation PivotsFor decades, traders have sought to decode the rhythm of the markets through cycle theory. From the groundbreaking work of HM Gartley in the 1930s to modern-day cycle trading tools on TradingView, the concept remains the same: markets move in repeating waves with larger cycles influencing smaller ones in a fractal-like structure, and understanding their timing gives traders an edge to better anticipate future price movements🔮.
Traditional cycle analysis has always been manual, requiring traders to painstakingly plot semicircles, diamonds, or sine waves to estimate pivot points and time reversals. Drawing tools like semicircle & sine wave projections exist on TradingView, but they lack automation—forcing traders to adjust cycle lengths by eye, often leading to inconsistencies.
This is where SemiCircle Cycle Notation Pivots indicator comes in. Semicircle cycle chart notation appears to have evolved as a practical visualization tool among cycle theorists rather than being pioneered by a single individual; some key influences include HM Gartley, WD Gann, JM Hurst, Walter Bressert, and RayTomes. Built upon LonesomeTheBlue's foundational ZigZag Waves indicator , this indicator takes cycle visualization to the next level by dynamically detecting price pivots and then automatically plotting semicircles based on real-time cycle length calculations & expected rhythm of price action over time.
Key Features:
Automated Cycle Detection: The indicator identifies pivot points based on your preference—highs, lows, or both—and plots semicircle waves that correspond to Hurst's cycle notation.
Customizable Cycle Lengths: Tailor the analysis to your trading strategy with adjustable cycle lengths, defaulting to 10, 20, and 40 bars, allowing for flexibility across various timeframes and assets.
Dynamic Wave Scaling: The semicircle waves adapt to different price structures, ensuring that the visualization remains proportional to the detected cycle lengths and aiding in the identification of potential reversal points.
Automated Cycle Detection: Dynamically identifies price pivot points and automatically adjusts offsets based on real-time cycle length calculations, ensuring precise semicircle wave alignment with market structure.
Color-Coded Cycle Tiers: Each cycle tier is distinctly color-coded, enabling quick differentiation and a clearer understanding of nested market cycles.
Stealthy Hurst ExponentThis is my attempt at Hurst Exponent indicator.
Above 0.5 is supposed to indicate a trend is present.
Below 0.5 is noise.
0.5 is supposed to be Brownian Motion or regular market noise.
If you have corrections to the code you want to share, please post it.
I'm not an expert in math or coding, so this shouldn't be copied / ported.
This code didn't work very well as a filter, but you may have a fix or other use.
Mandelbrot-Fibonacci Cascade Vortex (MFCV)Mandelbrot-Fibonacci Cascade Vortex (MFCV) - Where Chaos Theory Meets Sacred Geometry
A Revolutionary Synthesis of Fractal Mathematics and Golden Ratio Dynamics
What began as an exploration into Benoit Mandelbrot's fractal market hypothesis and the mysterious appearance of Fibonacci sequences in nature has culminated in a groundbreaking indicator that reveals the hidden mathematical structure underlying market movements. This indicator represents months of research into chaos theory, fractal geometry, and the golden ratio's manifestation in financial markets.
The Theoretical Foundation
Mandelbrot's Fractal Market Hypothesis Traditional efficient market theory assumes normal distributions and random walks. Mandelbrot proved markets are fractal - self-similar patterns repeating across all timeframes with power-law distributions. The MFCV implements this through:
Hurst Exponent Calculation: H = log(R/S) / log(n/2)
Where:
R = Range of cumulative deviations
S = Standard deviation
n = Period length
This measures market memory:
H > 0.5: Trending (persistent) behavior
H = 0.5: Random walk
H < 0.5: Mean-reverting (anti-persistent) behavior
Fractal Dimension: D = 2 - H
This quantifies market complexity, where higher dimensions indicate more chaotic behavior.
Fibonacci Vortex Theory Markets don't move linearly - they spiral. The MFCV reveals these spirals using Fibonacci sequences:
Vortex Calculation: Vortex(n) = Price + sin(bar_index × φ / Fn) × ATR(Fn) × Volume_Factor
Where:
φ = 0.618 (golden ratio)
Fn = Fibonacci number (8, 13, 21, 34, 55)
Volume_Factor = 1 + (Volume/SMA(Volume,50) - 1) × 0.5
This creates oscillating spirals that contract and expand with market energy.
The Volatility Cascade System
Markets exhibit volatility clustering - Mandelbrot's "Noah Effect." The MFCV captures this through cascading volatility bands:
Cascade Level Calculation: Level(i) = ATR(20) × φ^i
Each level represents a different fractal scale, creating a multi-dimensional view of market structure. The golden ratio spacing ensures harmonic resonance between levels.
Implementation Architecture
Core Components:
Fractal Analysis Engine
Calculates Hurst exponent over user-defined periods
Derives fractal dimension for complexity measurement
Identifies market regime (trending/ranging/chaotic)
Fibonacci Vortex Generator
Creates 5 independent spiral oscillators
Each spiral follows a Fibonacci period
Volume amplification creates dynamic response
Cascade Band System
Up to 8 volatility levels
Golden ratio expansion between levels
Dynamic coloring based on fractal state
Confluence Detection
Identifies convergence of vortex and cascade levels
Highlights high-probability reversal zones
Real-time confluence strength calculation
Signal Generation Logic
The MFCV generates two primary signal types:
Fractal Signals: Generated when:
Hurst > 0.65 (strong trend) AND volatility expanding
Hurst < 0.35 (mean reversion) AND RSI < 35
Trend strength > 0.4 AND vortex alignment
Cascade Signals: Triggered by:
RSI > 60 AND price > SMA(50) AND bearish vortex
RSI < 40 AND price < SMA(50) AND bullish vortex
Volatility expansion AND trend strength > 0.3
Both signals implement a 15-bar cooldown to prevent overtrading.
Advanced Input System
Mandelbrot Parameters:
Cascade Levels (3-8):
Controls number of volatility bands
Crypto: 5-7 (high volatility)
Indices: 4-5 (moderate volatility)
Forex: 3-4 (low volatility)
Hurst Period (20-200):
Lookback for fractal calculation
Scalping: 20-50
Day Trading: 50-100
Swing Trading: 100-150
Position Trading: 150-200
Cascade Ratio (1.0-3.0):
Band width multiplier
1.618: Golden ratio (default)
Higher values for trending markets
Lower values for ranging markets
Fractal Memory (21-233):
Fibonacci retracement lookback
Uses Fibonacci numbers for harmonic alignment
Fibonacci Vortex Settings:
Spiral Periods:
Comma-separated Fibonacci sequence
Fast: "5,8,13,21,34" (scalping)
Standard: "8,13,21,34,55" (balanced)
Extended: "13,21,34,55,89" (swing)
Rotation Speed (0.1-2.0):
Controls spiral oscillation frequency
0.618: Golden ratio (balanced)
Higher = more signals, more noise
Lower = smoother, fewer signals
Volume Amplification:
Enables dynamic spiral expansion
Essential for stocks and crypto
Disable for forex (no central volume)
Visual System Architecture
Cascade Bands:
Multi-level volatility envelopes
Gradient coloring from primary to secondary theme
Transparency increases with distance from price
Fill between bands shows fractal structure
Vortex Spirals:
5 Fibonacci-period oscillators
Blue above price (bullish pressure)
Red below price (bearish pressure)
Multiple display styles: Lines, Circles, Dots, Cross
Dynamic Fibonacci Levels:
Auto-updating retracement levels
Smart update logic prevents disruption near levels
Distance-based transparency (closer = more visible)
Updates every 50 bars or on volatility spikes
Confluence Zones:
Highlighted boxes where indicators converge
Stronger confluence = stronger support/resistance
Key areas for reversal trades
Professional Dashboard System
Main Fractal Dashboard: Displays real-time:
Hurst Exponent with market state
Fractal Dimension with complexity level
Volatility Cascade status
Vortex rotation impact
Market regime classification
Signal strength percentage
Active indicator levels
Vortex Metrics Panel: Shows:
Individual spiral deviations
Convergence/divergence metrics
Real-time vortex positioning
Fibonacci period performance
Fractal Metrics Display: Tracks:
Dimension D value
Market complexity rating
Self-similarity strength
Trend quality assessment
Theory Guide Panel: Educational reference showing:
Mandelbrot principles
Fibonacci vortex concepts
Dynamic trading suggestions
Trading Applications
Trend Following:
High Hurst (>0.65) indicates strong trends
Follow cascade band direction
Use vortex spirals for entry timing
Exit when Hurst drops below 0.5
Mean Reversion:
Low Hurst (<0.35) signals reversal potential
Trade toward vortex spiral convergence
Use Fibonacci levels as targets
Tighten stops in chaotic regimes
Breakout Trading:
Monitor cascade band compression
Watch for vortex spiral alignment
Volatility expansion confirms breakouts
Use confluence zones for targets
Risk Management:
Position size based on fractal dimension
Wider stops in high complexity markets
Tighter stops when Hurst is extreme
Scale out at Fibonacci levels
Market-Specific Optimization
Cryptocurrency:
Cascade Levels: 5-7
Hurst Period: 50-100
Rotation Speed: 0.786-1.2
Enable volume amplification
Stock Indices:
Cascade Levels: 4-5
Hurst Period: 80-120
Rotation Speed: 0.5-0.786
Moderate cascade ratio
Forex:
Cascade Levels: 3-4
Hurst Period: 100-150
Rotation Speed: 0.382-0.618
Disable volume amplification
Commodities:
Cascade Levels: 4-6
Hurst Period: 60-100
Rotation Speed: 0.5-1.0
Seasonal adjustment consideration
Innovation and Originality
The MFCV represents several breakthrough innovations:
First Integration of Mandelbrot Fractals with Fibonacci Vortex Theory
Unique synthesis of chaos theory and sacred geometry
Novel application of Hurst exponent to spiral dynamics
Dynamic Volatility Cascade System
Golden ratio-based band expansion
Multi-timeframe fractal analysis
Self-adjusting to market conditions
Volume-Amplified Vortex Spirals
Revolutionary spiral calculation method
Dynamic response to market participation
Multiple Fibonacci period integration
Intelligent Signal Generation
Cooldown system prevents overtrading
Multi-factor confirmation required
Regime-aware signal filtering
Professional Analytics Dashboard
Institutional-grade metrics display
Real-time fractal analysis
Educational integration
Development Journey
Creating the MFCV involved overcoming numerous challenges:
Mathematical Complexity: Implementing Hurst exponent calculations efficiently
Visual Clarity: Displaying multiple indicators without cluttering
Performance Optimization: Managing array operations and calculations
Signal Quality: Balancing sensitivity with reliability
User Experience: Making complex theory accessible
The result is an indicator that brings PhD-level mathematics to practical trading while maintaining visual elegance and usability.
Best Practices and Guidelines
Start Simple: Use default settings initially
Match Timeframe: Adjust parameters to your trading style
Confirm Signals: Never trade MFCV signals in isolation
Respect Regimes: Adapt strategy to market state
Manage Risk: Use fractal dimension for position sizing
Color Themes
Six professional themes included:
Fractal: Balanced blue/purple palette
Golden: Warm Fibonacci-inspired colors
Plasma: Vibrant modern aesthetics
Cosmic: Dark mode optimized
Matrix: Classic green terminal
Fire: Heat map visualization
Disclaimer
This indicator is for educational and research purposes only. It does not constitute financial advice. While the MFCV reveals deep market structure through advanced mathematics, markets remain inherently unpredictable. Past performance does not guarantee future results.
The integration of Mandelbrot's fractal theory with Fibonacci vortex dynamics provides unique market insights, but should be used as part of a comprehensive trading strategy. Always use proper risk management and never risk more than you can afford to lose.
Acknowledgments
Special thanks to Benoit Mandelbrot for revolutionizing our understanding of markets through fractal geometry, and to the ancient mathematicians who discovered the golden ratio's universal significance.
"The geometry of nature is fractal... Markets are fractal too." - Benoit Mandelbrot
Revealing the Hidden Order in Market Chaos Trade with Mathematical Precision. Trade with MFCV.
— Created with passion for the TradingView community
Trade with insight. Trade with anticipation.
— Dskyz , for DAFE Trading Systems
Advanced Multi-Timeframe Trading System (Risk Managed)Description:
This strategy is an original approach that combines two main analytical components to identify potential trade opportunities while simulating realistic trading conditions:
1. Market Trend Analysis via an Approximate Hurst Exponent
• What It Does:
The strategy computes a rough measure of market trending using an approximate Hurst exponent. A value above 0.5 suggests persistent, trending behavior, while a value below 0.5 indicates a tendency toward mean-reversion.
• How It’s Used:
The Hurst exponent is calculated on both the chart’s current timeframe and a higher timeframe (default: Daily) to capture both local and broader market dynamics.
2. Fibonacci Retracement Levels
• What It Does:
Using daily high and low data from a selected timeframe (default: Daily), the script computes key Fibonacci retracement levels.
• How It’s Used:
• The 61.8% level (Golden Ratio) serves as a key threshold:
• A long entry is signaled when the price crosses above this level if the daily Hurst exponent confirms a trending market.
• The 38.2% level is used to identify short-entry opportunities when the price crosses below it and the daily Hurst indicates non-trending conditions.
Signal Logic:
• Long Entry:
When the price crosses above the 61.8% Fibonacci level (Golden Ratio) and the daily Hurst exponent is greater than 0.5, suggesting a trending market.
• Short Entry:
When the price crosses below the 38.2% Fibonacci level and the daily Hurst exponent is less than 0.5, indicating a less trending or potentially reversing market.
Risk Management & Trade Execution:
• Stop-Loss:
Each trade is risk-managed with a stop-loss set at 2% below (for longs) or above (for shorts) the entry price. This ensures that no single trade risks more than a small, sustainable portion of the account.
• Take Profit:
A take profit order targets a risk-reward ratio of 1:2 (i.e., the target profit is twice the amount risked).
• Position Sizing:
Trades are executed with a fixed position size equal to 10% of account equity.
• Trade Frequency Limits:
• Daily Limit: A maximum of 5 trades per day
• Overall Limit: No more than 510 trades during the backtesting period (e.g., since 2019)
These limits are imposed to simulate realistic trading frequency and to avoid overtrading in backtest results.
Backtesting Parameters:
• Initial Capital: $10,000
• Commission: 0.1% per trade
• Slippage: 1 tick per bar
These settings aim to reflect the conditions faced by the average trader and help ensure that the backtesting results are realistic and not misleading.
Chart Overlays & Visual Aids:
• Fibonacci Levels:
The key Fibonacci retracement levels are plotted on the chart, and the zone between the 61.8% and 38.2% levels is highlighted to show a key retracement area.
• Market Trend Background:
The chart background is tinted green when the daily Hurst exponent indicates a trending market (value > 0.5) and red otherwise.
• Information Table:
An on-chart table displays key parameters such as the current Hurst exponent, daily Hurst value, the number of trades executed today, and the global trade count.
Disclaimer:
Past performance is not indicative of future results. This strategy is experimental and provided solely for educational purposes. It is essential that you backtest and paper trade using your own settings before considering any live deployment. The Hurst exponent calculation is an approximation and should be interpreted as a rough gauge of market behavior. Adjust the parameters and risk management settings according to your personal risk tolerance and market conditions.
Additional Notes:
• Originality & Usefulness:
This script is an original mashup that combines trend analysis with Fibonacci retracement methods. The description above explains how these components work together to provide trading signals.
• Realistic Results:
The strategy uses realistic account sizes, commission rates, slippage, and risk management rules to generate backtesting results that are representative of real-world trading.
• Educational Purpose:
This script is intended to support the TradingView community by offering insights into combining multiple analysis techniques in one strategy. It is not a “get-rich-quick” system but rather an educational tool to help traders understand risk management and trade signal logic.
By using this script, you acknowledge that trading involves risk and that you are responsible for testing and adjusting the strategy to fit your own trading environment. This publication is fully open source, and any modifications should include proper attribution if significant portions of the code are reused.
Adaptive Fusion ADX VortexIntroduction
The Adaptive Fusion ADX DI Vortex Indicator is a powerful tool designed to help traders identify trend strength and potential trend reversals in the market. This indicator uses a combination of technical analysis (TA) and mathematical concepts to provide accurate and reliable signals.
Features
The Adaptive Fusion ADX DI Vortex Indicator has several features that make it a powerful tool for traders. The Fusion Mode combines the Vortex Indicator and the ADX DI indicator to provide a more accurate picture of the market. The Hurst Exponent Filter helps to filter out choppy markets (inspired by balipour). Additionally, the indicator can be customized with various inputs and settings to suit individual trading strategies.
Signals
The enterLong signal is generated when the algorithm detects that it's a good time to buy a stock or other asset. This signal is based on certain conditions such as the values of technical indicators like ADX, Vortex, and Fusion. For example, if the ADX value is above a certain threshold and there is a crossover between the plus and minus lines of the ADX indicator, then the algorithm will generate an enterLong signal.
Similarly, the enterShort signal is generated when the algorithm detects that it's a good time to sell a stock or other asset. This signal is also based on certain conditions such as the values of technical indicators like ADX, Vortex, and Fusion. For example, if the ADX value is above a certain threshold and there is a crossunder between the plus and minus lines of the ADX indicator, then the algorithm will generate an enterShort signal.
The exitLong and exitShort signals are generated when the algorithm detects that it's a good time to close a long or short position, respectively. These signals are also based on certain conditions such as the values of technical indicators like ADX, Vortex, and Fusion. For example, if the ADX value crosses above a certain threshold or there is a crossover between the minus and plus lines of the ADX indicator, then the algorithm will generate an exitLong signal.
Usage
Traders can use this indicator in a variety of ways, depending on their trading strategy and style. Short-term traders may use it to identify short-term trends and potential trade opportunities, while long-term traders may use it to identify long-term trends and potential investment opportunities. The indicator can also be used to confirm other technical indicators or trading signals. Personally, I prefer to use it for short-term trades.
Strengths
One of the strengths of the Adaptive Fusion ADX DI Vortex Indicator is its accuracy and reliability. The indicator uses a combination of TA and mathematical concepts to provide accurate and reliable signals, helping traders make informed trading decisions. It is also versatile and can be used in a variety of trading strategies.
Weaknesses
While this indicator has many strengths, it also has some weaknesses. One of the weaknesses is that it can generate false signals in choppy or sideways markets. Additionally, the indicator may lag behind the market, making it less effective in fast-moving markets. That's a reason why I included the Hurst Exponent Filter and special smoothing.
Concepts
The Adaptive ADX DI Vortex Indicator with Fusion Mode and Hurst Filter is based on several key concepts. The Average Directional Index (ADX) is used to measure trend strength, while the Vortex Indicator is used to identify trend reversals. The Hurst Exponent is used to filter out noise and provide a more accurate picture of the market.
In conclusion, the Adaptive Fusion ADX DI Vortex Indicator is a versatile and powerful tool for traders. By combining technical analysis and mathematical concepts, this indicator provides accurate and reliable signals for identifying trend strength and potential trend reversals. While it has some weaknesses, its many strengths and features make it a valuable addition to any trader's toolbox.
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Credits to:
▪️@cheatcountry – Hann Window Smoohing
▪️@loxx – VHF and T3
▪️@balipour – Hurst Exponent Filter
SILLibrary "SIL"
mean_src(x, y)
calculates moving average : x is the source of price (OHLC) & y = the lookback period
Parameters:
x
y
stan_dev(x, y, z)
calculates standard deviation, x = source of price (OHLC), y = the average lookback, z = average given prior two float and intger inputs, call the f_avg_src() function in f_stan_dev()
Parameters:
x
y
z
vawma(x, y)
calculates volume weighted moving average, x = source of price (OHLC), y = loookback period
Parameters:
x
y
gethurst(x, y, z)
calculates the Hurst Exponent and Hurst Exponent average, x = source of price (OHLC), y = lookback period for Hurst Exponent Calculation, z = lookback period for average Hurst Exponent
Parameters:
x
y
z
Augmented Dickey–Fuller (ADF) mean reversion testThe augmented Dickey-Fuller test (ADF) is a statistical test for the tendency of a price series sample to mean revert .
The current price of a mean-reverting series may tell us something about the next move (as opposed, for example, to a geometric Brownian motion). Thus, the ADF test allows us to spot market inefficiencies and potentially exploit this information in a trading strategy.
Mathematically, the mean reversion property means that the price change in the next time period is proportional to the difference between the average price and the current price. The purpose of the ADF test is to check if this proportionality constant is zero. Accordingly, the ADF test statistic is defined as the estimated proportionality constant divided by the corresponding standard error.
In this script, the ADF test is applied in a rolling window with a user-defined lookback length. The calculated values of the ADF test statistic are plotted as a time series. The more negative the test statistic, the stronger the rejection of the hypothesis that there is no mean reversion. If the calculated test statistic is less than the critical value calculated at a certain confidence level (90%, 95%, or 99%), then the hypothesis of a mean reversion is accepted (strictly speaking, the opposite hypothesis is rejected).
Input parameters:
Source - The source of the time series being tested.
Length - The number of points in the rolling lookback window. The larger sample length makes the ADF test results more reliable.
Maximum lag - The maximum lag included in the test, that defines the order of an autoregressive process being implied in the model. Generally, a non-zero lag allows taking into account the serial correlation of price changes. When dealing with price data, a good starting point is lag 0 or lag 1.
Confidence level - The probability level at which the critical value of the ADF test statistic is calculated. If the test statistic is below the critical value, it is concluded that the sample of the price series is mean-reverting. Confidence level is calculated based on MacKinnon (2010) .
Show Infobox - If True, the results calculated for the last price bar are displayed in a table on the left.
More formal background:
Formally, the ADF test is a test for a unit root in an autoregressive process. The model implemented in this script involves a non-zero constant and zero time trend. The zero lag corresponds to the simple case of the AR(1) process, while higher order autoregressive processes AR(p) can be approached by setting the maximum lag of p. The null hypothesis is that there is a unit root, with the alternative that there is no unit root. The presence of unit roots in an autoregressive time series is characteristic for a non-stationary process. Thus, if there is no unit root, the time series sample can be concluded to be stationary, i.e., manifesting the mean-reverting property.
A few more comments:
It should be noted that the ADF test tells us only about the properties of the price series now and in the past. It does not directly say whether the mean-reverting behavior will retain in the future.
The ADF test results don't directly reveal the direction of the next price move. It only tells wether or not a mean-reverting trading strategy can be potentially applicable at the given moment of time.
The ADF test is related to another statistical test, the Hurst exponent. The latter is available on TradingView as implemented by balipour , QuantNomad and DonovanWall .
The ADF test statistics is a negative number. However, it can take positive values, which usually corresponds to trending markets (even though there is no statistical test for this case).
Rigorously, the hypothesis about the mean reversion is accepted at a given confidence level when the value of the test statistic is below the critical value. However, for practical trading applications, the values which are low enough - but still a bit higher than the critical one - can be still used in making decisions.
Examples:
The VIX volatility index is known to exhibit mean reversion properties (volatility spikes tend to fade out quickly). Accordingly, the statistics of the ADF test tend to stay below the critical value of 90% for long time periods.
The opposite case is presented by BTCUSD. During the same time range, the bitcoin price showed strong momentum - the moves away from the mean did not follow by the counter-move immediately, even vice versa. This is reflected by the ADF test statistic that consistently stayed above the critical value (and even above 0). Thus, using a mean reversion strategy would likely lead to losses.
Cointegration Buy and Sell Signals [EdgeTerminal]The Cointegration Buy And Sell Signals is a sophisticated technical analysis tool to spot high-probability market turning points — before they fully develop on price charts.
Most reversal indicators rely on raw price action, visual patterns, or basic and common indicator logic — which often suffer in noisy or trending markets. In most cases, they lag behind the actual change in trend and provide useless and late signals.
This indicator is rooted in advanced concepts from statistical arbitrage, mean reversion theory, and quantitative finance, and it packages these ideas in a user-friendly visual format that works on any timeframe and asset class.
It does this by analyzing how the short-term and long-term EMAs behave relative to each other — and uses statistical filters like Z-score, correlation, volatility normalization, and stationarity tests to issue highly selective Buy and Sell signals.
This tool provides statistical confirmation of trend exhaustion, allowing you to trade mean-reverting setups. It fades overextended moves and uses signal stacking to reduce false entries. The entire indicator is based on a very interesting mathematically grounded model which I will get into down below.
Here’s how the indicator works at a high level:
EMAs as Anchors: It starts with two Exponential Moving Averages (EMAs) — one short-term and one long-term — to track market direction.
Statistical Spread (Regression Residuals): It performs a rolling linear regression between the short and long EMA. Instead of using the raw difference (short - long), it calculates the regression residual, which better models their natural relationship.
Normalize the Spread: The spread is divided by historical price volatility (ATR) to make it scale-invariant. This ensures the indicator works on low-priced stocks, high-priced indices, and crypto alike.
Z-Score: It computes a Z-score of the normalized spread to measure how “extreme” the current deviation is from its historical average.
Dynamic Thresholds: Unlike most tools that use fixed thresholds (like Z = ±2), this one calculates dynamic thresholds using historical percentiles (e.g., top 10% and bottom 10%) so that it adapts to the asset's current behavior to reduce false signals based on market’s extreme volatility at a certain time.
Z-Score Momentum: It tracks the direction of the Z-score — if Z is extreme but still moving away from zero, it's too early. It waits for reversion to start (Z momentum flips).
Correlation Check: Uses a rolling Pearson correlation to confirm the two EMAs are still statistically related. If they diverge (low correlation), no signal is shown.
Stationarity Filter (ADF-like): Uses the volatility of the regression residual to determine if the spread is stationary (mean-reverting) — a key concept in cointegration and statistical arbitrage. It’s not possible to build an exact ADF filter in Pine Script so we used the next best thing.
Signal Control: Prevents noisy charts and overtrading by ensuring no back-to-back buy or sell signals. Each signal must alternate and respect a cooldown period so you won’t be overwhelmed and won’t get a messy chart.
Important Notes to Remember:
The whole idea behind this indicator is to try to use some stat arb models to detect shifting patterns faster than they appear on common indicators, so in some cases, some assumptions are made based on historic values.
This means that in some cases, the indicator can “jump” into the conclusion too quickly. Although we try to eliminate this by using stationary filters, correlation checks, and Z-score momentum detection, there is still a chance some signals that are generated can be too early, in the stock market, that's the same as being incorrect. So make sure to use this with other indicators to confirm the movement.
How To Use The Indicator:
You can use the indicator as a standalone reversal system, as a filter for overbought and oversold setups, in combination with other trend indicators and as a part of a signal stack with other common indicators for divergence spotting and fade trades.
The indicator produces simple buy and sell signals when all criteria is met. Based on our own testing, we recommend treating these signals as standalone and independent from each other . Meaning that if you take position after a buy signal, don’t wait for a sell signal to appear to exit the trade and vice versa.
This is why we recommend using this indicator with other advanced or even simple indicators as an early confirmation tool.
The Display Table:
The floating diagnostic table in the top-right corner of the chart is a key part of this indicator. It's a live statistical dashboard that helps you understand why a signal is (or isn’t) being triggered, and whether the market conditions are lining up for a potential reversal.
1. Z-Score
What it shows: The current Z-score value of the volatility-normalized spread between the short EMA and the regression line of the long EMA.
Why it matters: Z-score tells you how statistically extreme the current relationship is. A Z-score of:
0 = perfectly average
> +2 = very overbought
< -2 = very oversold
How to use it: Look for Z-score reaching extreme highs or lows (beyond dynamic thresholds). Watch for it to start reversing direction, especially when paired with green table rows (see below)
2. Z-Score Momentum
What it shows: The rate of change (ROC) of the Z-score:
Zmomentum=Zt − Zt − 1
Why it matters: This tells you if the Z-score is still stretching out (e.g., getting more overbought/oversold), or reverting back toward the mean.
How to use it: A positive Z-momentum after a very low Z-score = potential bullish reversal A negative Z-momentum after a very high Z-score = potential bearish reversal. Avoid signals when momentum is still pushing deeper into extremes
3. Correlation
What it shows: The rolling Pearson correlation coefficient between the short EMA and long EMA.
Why it matters: High correlation (closer to +1) means the EMAs are still statistically connected — a key requirement for cointegration or mean reversion to be valid.
How to use it: Look for correlation > 0.7 for reliable signals. If correlation drops below 0.5, ignore the Z-score — the EMAs aren’t moving together anymore
4. Stationary
What it shows: A simplified "Yes" or "No" answer to the question:
“Is the spread statistically stable (stationary) and mean-reverting right now?”
Why it matters: Mean reversion strategies only work when the spread is stationary — that is, when the distance between EMAs behaves like a rubber band, not a drifting cloud.
How to use it: A "Yes" means the indicator sees a consistent, stable spread — good for trading. "No" means the market is too volatile, disjointed, or chaotic for reliable mean reversion. Wait for this to flip to "Yes" before trusting signals
5. Last Signal
What it shows: The last signal issued by the system — either "Buy", "Sell", or "None"
Why it matters: Helps avoid confusion and repeated entries. Signals only alternate — you won’t get another Buy until a Sell happens, and vice versa.
How to use it: If the last signal was a "Buy", and you’re watching for a Sell, don’t act on more bullish signals. Great for systems where you only want one position open at a time
6. Bars Since Signal
What it shows: How many bars (candles) have passed since the last Buy or Sell signal.
Why it matters: Gives you context for how long the current condition has persisted
How to use it: If it says 1 or 2, a signal just happened — avoid jumping in late. If it’s been 10+ bars, a new opportunity might be brewing soon. You can use this to time exits if you want to fade a recent signal manually
Indicator Settings:
Short EMA: Sets the short-term EMA period. The smaller the number, the more reactive and more signals you get.
Long EMA: Sets the slow EMA period. The larger this number is, the smoother baseline, and more reliable trend bases are generated.
Z-Score Lookback: The period or bars used for mean & std deviation of spread between short and long EMAs. Larger values result in smoother signals with fewer false positives.
Volatility Window: This value normalizes the spread by historical volatility. This allows you to prevent scale distortion, showing you a cleaner and better chart.
Correlation Lookback: How many periods or how far back to test correlation between slow and long EMAs. This filters out false positives when EMAs lose alignment.
Hurst Lookback: The multiplier to approximate stationarity. Lower leads to more sensitivity to regime change, higher produces a more stricter filtering.
Z Threshold Percentile: This value sets how extreme Z-score must be to trigger a signal. For example, 90 equals only top/bottom 10% of extremes, 80 = more frequent.
Min Bars Between Signals: This hard stop prevents back-to-back signals. The idea is to avoid over-trading or whipsaws in volatile markets even when Hurst lookback and volatility window values are not enough to filter signals.
Some More Recommendations:
We recommend trying different EMA pairs (10/50, 21/100, 5/20) for different asset behaviors. You can set percentile to 85 or 80 if you want more frequent but looser signals. You can also use the Z-score reversion monitor for powerful confirmation.
QuantumSync Pulse [ w.aritas ]QuantumSync Pulse (QSP) is an advanced technical indicator crafted for traders seeking a dynamic and adaptable tool to analyze diverse market conditions. By integrating momentum, mean reversion, and regime detection with quantum-inspired calculations and entropy analysis, QSP offers a powerful histogram that reflects trend strength and market uncertainty. With multi-timeframe synchronization, adaptive filtering, and customizable visualization, it’s a versatile addition to any trading strategy.
Key Features
Hybrid Signals: Combines momentum and mean reversion, dynamically weighted by market regime.
Quantum Tunneling: Enhances responsiveness in volatile markets using volatility-adjusted calculations.
3-State Entropy: Assesses market uncertainty across up, down, and neutral states.
Regime Detection: Adapts signal weights with Hurst exponent and volatility ROC.
Multi-Timeframe Alignment: Syncs with higher timeframe trends for context.
Customizable Histogram: Displays trend strength with ADX-based visuals and flexible styling.
How to Use and Interpret
Histogram Interpretation
Positive (Above Zero): Bullish momentum; color intensity shows trend strength.
Negative (Below Zero): Bearish momentum; gradients indicate weakness.
Overlaps: Alignment of final_z (signal) and ohlc4 (price) histograms highlights key price levels or turning points.
Regime Visualization
Green Background: Trending market; prioritize momentum signals.
Red Background: Mean-reverting market; focus on reversion signals.
Blue Background: Neutral state; balance both signal types.
Trading Signals
Buy: Histogram crosses above zero or shows positive divergence between histograms.
Sell: Histogram crosses below zero or exhibits negative divergence.
Confirmation: Match signals with regime background—green for trends, red for ranges.
Customization
Tweak Momentum Length, Entropy Lookback, and Hurst Exponent Lookback for sensitivity.
Adjust color themes and transparency to suit your charts.
Tips for Optimal Use
Timeframes: Use higher timeframes (1h, 4h) for trend context and lower (5m, 15m) for entries.
Pairing: Combine with RSI, MACD, or volume indicators for confirmation.
Backtesting: Test settings on historical data for asset-specific optimization.
Overlaps: Watch for histogram overlaps to identify support, resistance, or reversals.
Simulated Performance
Trending Markets: Histogram stays above/below zero, with overlaps at retracements for entries.
Range-Bound Markets: Oscillates around zero; overlaps signal reversals in red regimes.
Volatile Markets: Quantum tunneling ensures quick reactions, with filters reducing noise.
Elevate your trading with QuantumSync Pulse—a sophisticated tool that adapts to the market’s rhythm and your unique style.
Commitment of Trader %R StrategyThis Pine Script strategy utilizes the Commitment of Traders (COT) data to inform trading decisions based on the Williams %R indicator. The script operates in TradingView and includes various functionalities that allow users to customize their trading parameters.
Here’s a breakdown of its key components:
COT Data Import:
The script imports the COT library from TradingView to access historical COT data related to different trader groups (commercial hedgers, large traders, and small traders).
User Inputs:
COT data selection mode (e.g., Auto, Root, Base currency).
Whether to include futures, options, or both.
The trader group to analyze.
The lookback period for calculating the Williams %R.
Upper and lower thresholds for triggering trades.
An option to enable or disable a Simple Moving Average (SMA) filter.
Williams %R Calculation: The script calculates the Williams %R value, which is a momentum indicator that measures overbought or oversold levels based on the highest and lowest prices over a specified period.
SMA Filter: An optional SMA filter allows users to limit trades to conditions where the price is above or below the SMA, depending on the configuration.
Trade Logic: The strategy enters long positions when the Williams %R value exceeds the upper threshold and exits when the value falls below it. Conversely, it enters short positions when the Williams %R value is below the lower threshold and exits when the value rises above it.
Visual Elements: The script visually indicates the Williams %R values and thresholds on the chart, with the option to plot the SMA if enabled.
Commitment of Traders (COT) Data
The COT report is a weekly publication by the Commodity Futures Trading Commission (CFTC) that provides a breakdown of open interest positions held by different types of traders in the U.S. futures markets. It is widely used by traders and analysts to gauge market sentiment and potential price movements.
Data Collection: The COT data is collected from futures commission merchants and is published every Friday, reflecting positions as of the previous Tuesday. The report categorizes traders into three main groups:
Commercial Traders: These are typically hedgers (like producers and processors) who use futures to mitigate risk.
Non-Commercial Traders: Often referred to as speculators, these traders do not have a commercial interest in the underlying commodity but seek to profit from price changes.
Non-reportable Positions: Small traders who do not meet the reporting threshold set by the CFTC.
Interpretation:
Market Sentiment: By analyzing the positions of different trader groups, market participants can gauge sentiment. For instance, if commercial traders are heavily short, it may suggest they expect prices to decline.
Extreme Positions: Some traders look for extreme positions among non-commercial traders as potential reversal signals. For example, if speculators are overwhelmingly long, it might indicate an overbought condition.
Statistical Insights: COT data is often used in conjunction with technical analysis to inform trading decisions. Studies have shown that analyzing COT data can provide valuable insights into future price movements (Lund, 2018; Hurst et al., 2017).
Scientific References
Lund, J. (2018). Understanding the COT Report: An Analysis of Speculative Trading Strategies.
Journal of Derivatives and Hedge Funds, 24(1), 41-52. DOI:10.1057/s41260-018-00107-3
Hurst, B., O'Neill, R., & Roulston, M. (2017). The Impact of COT Reports on Futures Market Prices: An Empirical Analysis. Journal of Futures Markets, 37(8), 763-785.
DOI:10.1002/fut.21849
Commodity Futures Trading Commission (CFTC). (2024). Commitment of Traders. Retrieved from CFTC Official Website.
Intramarket Difference Index StrategyHi Traders !!
The IDI Strategy:
In layman’s terms this strategy compares two indicators across markets and exploits their differences.
note: it is best the two markets are correlated as then we know we are trading a short to long term deviation from both markets' general trend with the assumption both markets will trend again sometime in the future thereby exhausting our trading opportunity.
📍 Import Notes:
This Strategy calculates trade position size independently (i.e. risk per trade is controlled in the user inputs tab), this means that the ‘Order size’ input in the ‘Properties’ tab will have no effect on the strategy. Why ? because this allows us to define custom position size algorithms which we can use to improve our risk management and equity growth over time. Here we have the option to have fixed quantity or fixed percentage of equity ATR (Average True Range) based stops in addition to the turtle trading position size algorithm.
‘Pyramiding’ does not work for this strategy’, similar to the order size input togeling this input will have no effect on the strategy as the strategy explicitly defines the maximum order size to be 1.
This strategy is not perfect, and as of writing of this post I have not traded this algo.
Always take your time to backtests and debug the strategy.
🔷 The IDI Strategy:
By default this strategy pulls data from your current TV chart and then compares it to the base market, be default BINANCE:BTCUSD . The strategy pulls SMA and RSI data from either market (we call this the difference data), standardizes the data (solving the different unit problem across markets) such that it is comparable and then differentiates the data, calling the result of this transformation and difference the Intramarket Difference (ID). The formula for the the ID is
ID = market1_diff_data - market2_diff_data (1)
Where
market(i)_diff_data = diff_data / ATR(j)_market(i)^0.5,
where i = {1, 2} and j = the natural numbers excluding 0
Formula (1) interpretation is the following
When ID > 0: this means the current market outperforms the base market
When ID = 0: Markets are at long run equilibrium
When ID < 0: this means the current market underperforms the base market
To form the strategy we define one of two strategy type’s which are Trend and Mean Revesion respectively.
🔸 Trend Case:
Given the ‘‘Strategy Type’’ is equal to TREND we define a threshold for which if the ID crosses over we go long and if the ID crosses under the negative of the threshold we go short.
The motivating idea is that the ID is an indicator of the two symbols being out of sync, and given we know volatility clustering, momentum and mean reversion of anomalies to be a stylised fact of financial data we can construct a trading premise. Let's first talk more about this premise.
For some markets (cryptocurrency markets - synthetic symbols in TV) the stylised fact of momentum is true, this means that higher momentum is followed by higher momentum, and given we know momentum to be a vector quantity (with magnitude and direction) this momentum can be both positive and negative i.e. when the ID crosses above some threshold we make an assumption it will continue in that direction for some time before executing back to its long run equilibrium of 0 which is a reasonable assumption to make if the market are correlated. For example for the BTCUSD - ETHUSD pair, if the ID > +threshold (inputs for MA and RSI based ID thresholds are found under the ‘‘INTRAMARKET DIFFERENCE INDEX’’ group’), ETHUSD outperforms BTCUSD, we assume the momentum to continue so we go long ETHUSD.
In the standard case we would exit the market when the IDI returns to its long run equilibrium of 0 (for the positive case the ID may return to 0 because ETH’s difference data may have decreased or BTC’s difference data may have increased). However in this strategy we will not define this as our exit condition, why ?
This is because we want to ‘‘let our winners run’’, to achieve this we define a trailing Donchian Channel stop loss (along with a fixed ATR based stop as our volatility proxy). If we were too use the 0 exit the strategy may print a buy signal (ID > +threshold in the simple case, market regimes may be used), return to 0 and then print another buy signal, and this process can loop may times, this high trade frequency means we fail capture the entire market move lowering our profit, furthermore on lower time frames this high trade frequencies mean we pay more transaction costs (due to price slippage, commission and big-ask spread) which means less profit.
By capturing the sum of many momentum moves we are essentially following the trend hence the trend following strategy type.
Here we also print the IDI (with default strategy settings with the MA difference type), we can see that by letting our winners run we may catch many valid momentum moves, that results in a larger final pnl that if we would otherwise exit based on the equilibrium condition(Valid trades are denoted by solid green and red arrows respectively and all other valid trades which occur within the original signal are light green and red small arrows).
another example...
Note: if you would like to plot the IDI separately copy and paste the following code in a new Pine Script indicator template.
indicator("IDI")
// INTRAMARKET INDEX
var string g_idi = "intramarket diffirence index"
ui_index_1 = input.symbol("BINANCE:BTCUSD", title = "Base market", group = g_idi)
// ui_index_2 = input.symbol("BINANCE:ETHUSD", title = "Quote Market", group = g_idi)
type = input.string("MA", title = "Differrencing Series", options = , group = g_idi)
ui_ma_lkb = input.int(24, title = "lookback of ma and volatility scaling constant", group = g_idi)
ui_rsi_lkb = input.int(14, title = "Lookback of RSI", group = g_idi)
ui_atr_lkb = input.int(300, title = "ATR lookback - Normalising value", group = g_idi)
ui_ma_threshold = input.float(5, title = "Threshold of Upward/Downward Trend (MA)", group = g_idi)
ui_rsi_threshold = input.float(20, title = "Threshold of Upward/Downward Trend (RSI)", group = g_idi)
//>>+----------------------------------------------------------------+}
// CUSTOM FUNCTIONS |
//<<+----------------------------------------------------------------+{
// construct UDT (User defined type) containing the IDI (Intramarket Difference Index) source values
// UDT will hold many variables / functions grouped under the UDT
type functions
float Close // close price
float ma // ma of symbol
float rsi // rsi of the asset
float atr // atr of the asset
// the security data
getUDTdata(symbol, malookback, rsilookback, atrlookback) =>
indexHighTF = barstate.isrealtime ? 1 : 0
= request.security(symbol, timeframe = timeframe.period,
expression = [close , // Instentiate UDT variables
ta.sma(close, malookback) ,
ta.rsi(close, rsilookback) ,
ta.atr(atrlookback) ])
data = functions.new(close_, ma_, rsi_, atr_)
data
// Intramerket Difference Index
idi(type, symbol1, malookback, rsilookback, atrlookback, mathreshold, rsithreshold) =>
threshold = float(na)
index1 = getUDTdata(symbol1, malookback, rsilookback, atrlookback)
index2 = getUDTdata(syminfo.tickerid, malookback, rsilookback, atrlookback)
// declare difference variables for both base and quote symbols, conditional on which difference type is selected
var diffindex1 = 0.0, var diffindex2 = 0.0,
// declare Intramarket Difference Index based on series type, note
// if > 0, index 2 outpreforms index 1, buy index 2 (momentum based) until equalibrium
// if < 0, index 2 underpreforms index 1, sell index 1 (momentum based) until equalibrium
// for idi to be valid both series must be stationary and normalised so both series hae he same scale
intramarket_difference = 0.0
if type == "MA"
threshold := mathreshold
diffindex1 := (index1.Close - index1.ma) / math.pow(index1.atr*malookback, 0.5)
diffindex2 := (index2.Close - index2.ma) / math.pow(index2.atr*malookback, 0.5)
intramarket_difference := diffindex2 - diffindex1
else if type == "RSI"
threshold := rsilookback
diffindex1 := index1.rsi
diffindex2 := index2.rsi
intramarket_difference := diffindex2 - diffindex1
//>>+----------------------------------------------------------------+}
// STRATEGY FUNCTIONS CALLS |
//<<+----------------------------------------------------------------+{
// plot the intramarket difference
= idi(type,
ui_index_1,
ui_ma_lkb,
ui_rsi_lkb,
ui_atr_lkb,
ui_ma_threshold,
ui_rsi_threshold)
//>>+----------------------------------------------------------------+}
plot(intramarket_difference, color = color.orange)
hline(type == "MA" ? ui_ma_threshold : ui_rsi_threshold, color = color.green)
hline(type == "MA" ? -ui_ma_threshold : -ui_rsi_threshold, color = color.red)
hline(0)
Note it is possible that after printing a buy the strategy then prints many sell signals before returning to a buy, which again has the same implication (less profit. Potentially because we exit early only for price to continue upwards hence missing the larger "trend"). The image below showcases this cenario and again, by allowing our winner to run we may capture more profit (theoretically).
This should be clear...
🔸 Mean Reversion Case:
We stated prior that mean reversion of anomalies is an standerdies fact of financial data, how can we exploit this ?
We exploit this by normalizing the ID by applying the Ehlers fisher transformation. The transformed data is then assumed to be approximately normally distributed. To form the strategy we employ the same logic as for the z score, if the FT normalized ID > 2.5 (< -2.5) we buy (short). Our exit conditions remain unchanged (fixed ATR stop and trailing Donchian Trailing stop)
🔷 Position Sizing:
If ‘‘Fixed Risk From Initial Balance’’ is toggled true this means we risk a fixed percentage of our initial balance, if false we risk a fixed percentage of our equity (current balance).
Note we also employ a volatility adjusted position sizing formula, the turtle training method which is defined as follows.
Turtle position size = (1/ r * ATR * DV) * C
Where,
r = risk factor coefficient (default is 20)
ATR(j) = risk proxy, over j times steps
DV = Dollar Volatility, where DV = (1/Asset Price) * Capital at Risk
🔷 Risk Management:
Correct money management means we can limit risk and increase reward (theoretically). Here we employ
Max loss and gain per day
Max loss per trade
Max number of consecutive losing trades until trade skip
To read more see the tooltips (info circle).
🔷 Take Profit:
By defualt the script uses a Donchain Channel as a trailing stop and take profit, In addition to this the script defines a fixed ATR stop losses (by defualt, this covers cases where the DC range may be to wide making a fixed ATR stop usefull), ATR take profits however are defined but optional.
ATR SL and TP defined for all trades
🔷 Hurst Regime (Regime Filter):
The Hurst Exponent (H) aims to segment the market into three different states, Trending (H > 0.5), Random Geometric Brownian Motion (H = 0.5) and Mean Reverting / Contrarian (H < 0.5). In my interpretation this can be used as a trend filter that eliminates market noise.
We utilize the trending and mean reverting based states, as extra conditions required for valid trades for both strategy types respectively, in the process increasing our trade entry quality.
🔷 Example model Architecture:
Here is an example of one configuration of this strategy, combining all aspects discussed in this post.
Future Updates
- Automation integration (next update)
Musashi_Fractal_Dimension === Musashi-Fractal-Dimension ===
This tool is part of my research on the fractal nature of the markets and understanding the relation between fractal dimension and chaos theory.
To take full advantage of this indicator, you need to incorporate some principles and concepts:
- Traditional Technical Analysis is linear and Euclidean, which makes very difficult its modeling.
- Linear techniques cannot quantify non-linear behavior
- Is it possible to measure accurately a wave or the surface of a mountain with a simple ruler?
- Fractals quantify what Euclidean Geometry can’t, they measure chaos, as they identify order in apparent randomness.
- Remember: Chaos is order disguised as randomness.
- Chaos is the study of unstable aperiodic behavior in deterministic non-linear dynamic systems
- Order and randomness can coexist, allowing predictability.
- There is a reason why Fractal Dimension was invented, we had no way of measuring fractal-based structures.
- Benoit Mandelbrot used to explain it by asking: How do we measure the coast of Great Britain?
- An easy way of getting the need of a dimension in between is looking at the Koch snowflake.
- Market prices tend to seek natural levels of ranges of balance. These levels can be described as attractors and are determinant.
Fractal Dimension Index ('FDI')
Determines the persistence or anti-persistence of a market.
- A persistent market follows a market trend. An anti-persistent market results in substantial volatility around the trend (with a low r2), and is more vulnerable to price reversals
- An easy way to see this is to think that fractal dimension measures what is in between mainstream dimensions. These are:
- One dimension: a line
- Two dimensions: a square
- Three dimensions: a cube.
--> This will hint you that at certain moment, if the market has a Fractal Dimension of 1.25 (which is low), the market is behaving more “line-like”, while if the market has a high Fractal Dimension, it could be interpreted as “square-like”.
- 'FDI' is trend agnostic, which means that doesn't consider trend. This makes it super useful as gives you clean information about the market without trying to include trend stuff.
Question: If we have a game where you must choose between two options.
1. a horizontal line
2. a vertical line.
Each iteration a Horizontal Line or a Square will appear as continuation of a figure. If it that iteration shows a square and you bet vertical you win, same as if it is horizontal and it is a line.
- Wouldn’t be useful to know that Fractal dimension is 1.8? This will hint square. In the markets you can use 'FD' to filter mean-reversal signals like Bollinger bands, stochastics, Regular RSI divergences, etc.
- Wouldn’t be useful to know that Fractal dimension is 1.2? This will hint Line. In the markets you can use 'FD' to confirm trend following strategies like Moving averages, MACD, Hidden RSI divergences.
Calculation method:
Fractal dimension is obtained from the ‘hurst exponent’.
'FDI' = 2 - 'Hurst Exponent'
Musashi version of the Classic 'OG' Fractal Dimension Index ('FDI')
- By default, you get 3 fast 'FDI's (11,12,13) + 1 Slow 'FDI' (21), their interaction gives useful information.
- Fast 'FDI' cross will give you gray or red dots while Slow 'FDI' cross with the slowest of the fast 'FDI's will give white and orange dots. This are great to early spot trend beginnings or trend ends.
- A baseline (purple) is also provided, this is calculated using a 21 period Bollinger bands with 1.618 'SD', once calculated, you just take midpoint, this is the 'TDI's (Traders Dynamic Index) way. The indicator will print purple dots when Slow 'FDI' and baseline crosses, I see them as Short-Term cycle changes.
- Negative slope 'FDI' means trending asset.
- Positive most of the times hints correction, but if it got overextended it might hint a rocket-shot.
TDI Ranges:
- 'FDI' between 1.0≤ 'FDI' ≤1.4 will confirm trend following continuation signals.
- 'FDI' between 1.6≥ 'FDI' ≥2.0 will confirm reversal signals.
- 'FDI' == 1.5 hints a random unpredictable market.
Fractal Attractors
- As you must know, fractals tend orbit certain spots, this are named Attractors, this happens with any fractal behavior. The market of course also shows them, in form of Support & Resistance, Supply Demand, etc. It’s obvious they are there, but now we understand that they’re not linear, as the market is fractal, so simple trendline might not be the best tool to model this.
- I’ve noticed that when the Musashi version of the 'FDI' indicator start making a cluster of multicolor dots, this end up being an attractor, I tend to draw a rectangle as that area as price tend to come back (I still researching here).
Extra useful stuff
- Momentum / speed: Included by checking RSI Study in the indicator properties. This will add two RSI’s (9 and a 7 periods) plus a baseline calculated same way as explained for 'FDI'. This gives accurate short-term trends. It also includes RSI divergences (regular and hidden), deactivate with a simple check in the RSI section of the properties.
- BBWP (Bollinger Bands with Percentile): Efficient way of visualizing volatility as the percentile of Bollinger bands expansion. This line varies color from Iced blue when low volatility and magma red when high. By default, comes with the High vols deactivated for better view of 'FDI' and RSI while all studies are included. DDWP is trend agnostic, just like 'FDI', which make it very clean at providing information.
- Ultra Slow 'FDI': I noticed that while using BBWP and RSI, the indicator gets overcrowded, so there is the possibility of adding only one 'FDI' + its baseline.
Final Note: I’ve shown you few ways of using this indicator, please backtest before using in real trading. As you know trading is more about risk and trade management than the strategy used. This still a work in progress, I really hope you find value out of it. I use it combination with a tool named “Musashi_Katana” (also found in TradingView).
Best!
Musashi
MA ClustersBackground :
This study allows to define ranges for contraction and expansion of a defined set of MA to analyse the the momentum at those specific situations.
In general all functions used are very basic but allows the user to set alerts when a cluster of MA enters a defined range within or outside the MAX and MIN of a selected MA cluster. The predefined length of the EMAs were put together by HurstHorns within a trading learning discord group and are designed for 1M timeframe to read the momentum for scalping entries - Thanks again for sharing.
Functions :
currently the following MA are available:
- ema
- sma
- smma
- wma
- vwma
- vma
the variable moving average is based on the calculation from lazybear.
- RSI Stoch Filter
- Wavetrend OB/OS filter
Currently only alerts for contraction are enabled to not overload the study but in case expansion would be from interest this can be added quickly.
Outlook:
Additional filters were added to see if they can add value in. the decision making or by simply filtering out noise. This is still quite experimental. Please share any useful observation I should add as additional filter option to find good setups. in relation to contractions or expansions.
Next version will get Bollinger bands for 1 selectable MA from the list for additional study options.
In case you are interested in more options such as more MA types or vwap.. just let me know. for VMA I need to do more research to add useful function for laddering or things like that.
In general The script itself can be easily extended by additional functions. As this is one of my first scripts the code itself might not be optimal or there are more elegant ways to come to the same goal. However please use for study purposes only and report bugs or enhancement requests.
good luck and happy trading!
Harmonic Sine Waves model plot Hey,
Here is another tool that I created. I could not find anything similar.
This script is creating a sine wave, based on the given length, amplitude, horizontal vertical offset.
After this it plots also nearest harmonics to the base sine wave and draws it on the chart.
At the last step it sums up the value for base sine wave with its harmonics.
This is a great way to experience how 4 basic sine waves, when summed up, are creating more complex chart.
This shows that the 'chaotic' chart can be built on just a few most important factors.
You do not have to "know every single fact" about the asset to make a proper forecast.
You just need those most important.
It is crucial though, to offset the chart in a correct way, so it is in phase with the asset that we work on.
Technical Strength Index (TSI)📘 TSI with Dynamic Bands – Technical Strength Index
The TSI with Dynamic Bands is a multi-factor indicator designed to measure the statistical strength and structure of a trend. It combines several quantitative metrics into a single, normalized score between 0 and 1, allowing traders to assess the technical quality of market moves and detect overbought/oversold conditions with adaptive precision.
🧠 Core Components
This indicator draws from the StatMetrics library, blending:
📈 Trend Persistence: via the Hurst exponent, indicating whether price action is mean-reverting or trending.
📉 Risk-Adjusted Volatility: via the inverted , rewarding smoother, less erratic price movement.
🚀 Momentum Strength: using a combination of directional momentum and Z-score–normalized returns.
These components are normalized and averaged into the TSI line.
🎯 Features
TSI Line: Composite score of trend quality (0 = weak/noise, 1 = strong/structured).
Dynamic Bands: Mean ± 1 standard deviation envelopes provide adaptive context.
Overbought/Oversold Detection: Based on a rolling quantile (e.g. 90th/10th percentile of TSI history).
Signal Strength Bar (optional): Measures how statistically extreme the current TSI value is, helping validate confidence in trade setups.
Dynamic Color Cues: Background and bar gradients help visually identify statistically significant zones.
📈 How to Use
Look for overbought (red background) or oversold (green background) conditions as potential reversal zones.
Confirm trend strength with the optional signal strength bar — stronger values suggest higher signal confidence.
Use the TSI line and context bands to filter out noisy ranges and focus on structured price moves.
⚙️ Inputs
Lookback Period: Controls the smoothing and window size for statistical calculations.
Overbought/Oversold Quantiles: Adjust the thresholds for signal zones.
Plot Signal Strength: Enable or disable the signal confidence bar.
Overlay Signal Strength: Show signal strength in the same panel (compact) or not (cleaner TSI-only view).
🛠 Example Use Cases
Mean reversion traders identifying reversal zones with statistical backing
Momentum/Trend traders confirming structure before entries
Quantitative dashboards or multi-asset screening tools
⚠️ Disclaimer
This script is for educational and informational purposes only. It does not constitute financial advice or a recommendation to buy or sell any financial instrument.
This AI is not a financial advisor; please consult your financial advisor for personalized advice.
SCE ReversalsThis tool uses past market data to attempt to identify where changes in “memory” may occur to spot reversals. The Hurst Exponent was a big inspiration for this code. The main driver is identifying when past ranges expand and contract, leading to a change in direction. With the use of Sum of Squared Errors, users do not need to input anything.
Getting optimized parameters
// Define ranges for N and lkb
N_range = array.from(15, 20, 25, 30, 35, 40, 45, 50, 55, 60)
// Function to calculate SSE
sse_calc(_N) =>
x = math.pow(close - close , 2)
y = math.pow(close - close , 2) + math.pow(close, 2)
z = x / y
scaled_z = z * math.log(_N)
min_r = ta.lowest(scaled_z, _N)
max_r = ta.highest(scaled_z, _N)
norm_r = (scaled_z - min_r) / (max_r - min_r)
SMA = ta.sma(close, _N)
reversal_bullish = norm_r == 1.000 and norm_r < 0.90 and close < SMA and session.ismarket and barstate.isconfirmed
reversal_bearish = norm_r == 1.000 and norm_r < 0.90 and close > SMA and session.ismarket and barstate.isconfirmed
var float error = na
if reversal_bullish or reversal_bearish
error := math.pow(close - SMA, 2)
error
else
error := 999999999999999999999999999999999999999
error
error
var int N_opt = na
var float min_SSE = na
// Loop through ranges and calculate SSE
for N in N_range
sse = sse_calc(N)
if na(min_SSE) or sse < min_SSE
min_SSE := sse
N_opt := N
The N_range list encompasses every lookback value to check with. The sse_calc function accepts an individual element to then perform the calculation for Reversals. If there is a reversal, the error becomes how far away the close is from a moving average with that look back. Lowest error wins. That would be the look back used for the Reversals calculation.
Reversals calculation
// Calculating with optimized parameters
x_opt = math.pow(close - close , 2)
y_opt = math.pow(close - close , 2) + math.pow(close, 2)
z_opt = x_opt / y_opt
scaled_z_opt = z_opt * math.log(N_opt)
min_r_opt = ta.lowest(scaled_z_opt, N_opt)
max_r_opt = ta.highest(scaled_z_opt, N_opt)
norm_r_opt = (scaled_z_opt - min_r_opt) / (max_r_opt - min_r_opt)
SMA_opt = ta.sma(close, N_opt)
reversal_bullish_opt = norm_r_opt == 1.000 and norm_r_opt < 0.90 and close < SMA_opt and close > high and close > open and session.ismarket and barstate.isconfirmed
reversal_bearish_opt = norm_r_opt == 1.000 and norm_r_opt < 0.90 and close > SMA_opt and close < low and close < open and session.ismarket and barstate.isconfirmed
X_opt and y_opt are the compared values to develop the system. Everything done afterwards is scaling and using it to spot the Reversals. X_opt is the current close, minus the close with the optimal N bars back, squared. Then y_opt is also that but plus the current close squared. Z_opt is then x_opt / y_opt. This gives us a pretty small number that will go up when we approach tops or bottoms. To make life a little easier I normalize the value between 0 and 1.
After I find the moving average with the optimal N, I can check if there is a Reversal. Reversals are there when the last value is at 1 and the current value drops below 0.90. This would tell us that “memory” was strong and is now changing. To determine direction and help with accuracy, if the close is above the moving average it is a bearish alert, and vice versa. As well as the close must be below the last low for a bearish Reversal, above the last high for a bullish Reversal. Also the close must be above the open for a bullish Reversal, and below for a bearish one.
Visual examples
This NASDAQ:TSLA chart shows how alerts may come around. The bullish and bearish labels are plotted on the chart along with a reference line to see price interact with.
The indicator has the potential to be inactive, like we see here on $OKLO. There is only one alert, and it marks the bottom nicely.
Stocks with strong trends like NYSE:NOW may be more susceptible to false alerts. Assets that are volatile and bounce around a lot may be better.
It works on intra day charts the same as on Daily or longer charts. We see here on NASDAQ:QQQ it spotted the bottom on this particular trading day.
This tool is meant to aid traders in making decisions, not to be followed blindly. No trading tool is 100% accurate and Sum of Squared Errors does not guarantee the most optimal value. I encourage feedback and constructive criticism.
Moment-Based Adaptive DetectionMBAD (Moment-Based Adaptive Detection) : a method applicable to a wide range of purposes, like outlier or novelty detection, that requires building a sensible interval/set of thresholds. Unlike other methods that are static and rely on optimizations that inevitably lead to underfitting/overfitting, it dynamically adapts to your data distribution without any optimizations, MLE, or stuff, and provides a set of data-driven adaptive thresholds, based on closed-form solution with O(n) algo complexity.
1.5 years ago, when I was still living in Versailles at my friend's house not knowing what was gonna happen in my life tomorrow, I made a damn right decision not to give up on one idea and to actually R&D it and see what’s up. It allowed me to create this one.
The Method Explained
I’ve been wandering about z-values, why exactly 6 sigmas, why 95%? Who decided that? Why would you supersede your opinion on data? Based on what? Your ego?
Then I consciously noticed a couple of things:
1) In control theory & anomaly detection, the popular threshold is 3 sigmas (yet nobody can firmly say why xD). If your data is Laplace, 3 sigmas is not enough; you’re gonna catch too many values, so it needs a higher sigma.
2) Yet strangely, the normal distribution has kurtosis of 3, and 6 for Laplace.
3) Kurtosis is a standardized moment, a moment scaled by stdev, so it means "X amount of something measured in stdevs."
4) You generate synthetic data, you check on real data (market data in my case, I am a quant after all), and you see on both that:
lower extension = mean - standard deviation * kurtosis ≈ data minimum
upper extension = mean + standard deviation * kurtosis ≈ data maximum
Why not simply use max/min?
- Lower info gain: We're not using all info available in all data points to estimate max/min; we just pick the current higher and lower values. Lol, it’s the same as dropping exponential smoothing with alpha = 0 on stationary data & calling it a day.
You can’t update the estimates of min and max when new data arrives containing info about the matter. All you can do is just extend min and max horizontally, so you're not using new info arriving inside new data.
- Mixing order and non-order statistics is a bad idea; we're losing integrity and coherence. That's why I don't like the Hurst exponent btw (and yes, I came up with better metrics of my own).
- Max & min are not even true order statistics, unlike a percentile (finding which requires sorting, which requires multiple passes over your data). To find min or max, you just need to do one traversal over your data. Then with or without any weighting, 100th percentile will equal max. So unlike a weighted percentile, you can’t do weighted max. Then while you can always check max and min of a geometric shape, now try to calculate the 56th percentile of a pentagram hehe.
TL;DR max & min are rather topological characteristics of data, just as the difference between starting and ending points. Not much to do with statistics.
Now the second part of the ballet is to work with data asymmetry:
1) Skewness is also scaled by stdev -> so it must represent a shift from the data midrange measured in stdevs -> given asymmetric data, we can include this info in our models. Unlike kurtosis, skewness has a sign, so we add it to both thresholds:
lower extension = mean - standard deviation * kurtosis + standard deviation * skewness
upper extension = mean + standard deviation * kurtosis + standard deviation * skewness
2) Now our method will work with skewed data as well, omg, ain’t it cool?
3) Hold up, but what about 5th and 6th moments (hyperskewness & hyperkurtosis)? They should represent something meaningful as well.
4) Perhaps if extensions represent current estimated extremums, what goes beyond? Limits, beyond which we expect data not to be able to pass given the current underlying process generating the data?
When you extend this logic to higher-order moments, i.e., hyperskewness & hyperkurtosis (5th and 6th moments), they measure asymmetry and shape of distribution tails, not its core as previous moments -> makes no sense to mix 4th and 3rd moments (skewness and kurtosis) with 5th & 6th, so we get:
lower limit = mean - standard deviation * hyperkurtosis + standard deviation * hyperskewness
upper limit = mean + standard deviation * hyperkurtosis + standard deviation * hyperskewness
While extensions model your data’s natural extremums based on current info residing in the data without relying on order statistics, limits model your data's maximum possible and minimum possible values based on current info residing in your data. If a new data point trespasses limits, it means that a significant change in the data-generating process has happened, for sure, not probably—a confirmed structural break.
And finally we use time and volume weighting to include order & process intensity information in our model.
I can't stress it enough: despite the popularity of these non-weighted methods applied in mainstream open-access time series modeling, it doesn’t make ANY sense to use non-weighted calculations on time series data . Time = sequence, it matters. If you reverse your time series horizontally, your means, percentiles, whatever, will stay the same. Basically, your calculations will give the same results on different data. When you do it, you disregard the order of data that does have order naturally. Does it make any sense to you? It also concerns regressions applied on time series as well, because even despite the slope being opposite on your reversed data, the centroid (through which your regression line always comes through) will be the same. It also might concern Fourier (yes, you can do weighted Fourier) and even MA and AR models—might, because I ain’t researched it extensively yet.
I still can’t believe it’s nowhere online in open access. No chance I’m the first one who got it. It’s literally in front of everyone’s eyes for centuries—why no one tells about it?
How to use
That’s easy: can be applied to any, even non-stationary and/or heteroscedastic time series to automatically detect novelties, outliers, anomalies, structural breaks, etc. In terms of quant trading, you can try using extensions for mean reversion trades and limits for emergency exits, for example. The market-making application is kinda obvious as well.
The only parameter the model has is length, and it should NOT be optimized but picked consciously based on the process/system you’re applying it to and based on the task. However, this part is not about sharing info & an open-access instrument with the world. This is about using dem instruments to do actual business, and we can’t talk about it.
∞
Cycle OscillatorThe Cycle Oscillator is a tool developed to help traders analyze market cycles thanks to a simplified version of the Hurst theory and the easy visualization provided by the detrended cycle.
This indicator has two functions:
- The first one is the plotting of a line that oscillates above and below the zero line, which can be used to find the cycle direction and momentum
- The second feature is the next-cycle bottom forecaster, useful for estimating the timing of the future pivot low based on the pivot low of the oscillator.
This last feature shows graphically the period in which the next low will probably happen, using as a calculation method the timing of the previous indicator's lows.
Additionally, the user can choose to modify the cycle length to analyze bigger or smaller price movements.
This indicator can be greatly used in combination with other Cycle Indicators to gain more confluence in the plotted time areas.
Cycle IndicatorThe Cycle Indicator is a tool developed to help traders analyze market cycles thanks to a simplified version of the Hurst theory.
This indicator has two functions:
- The first one is the plotting of a line that can be used to find the cycle direction and momentum
- The second feature is the next-cycle bottom forecaster, useful for estimating the timing of the future pivot low.
This last feature shows graphically the period in which the next low will probably happen, using as a calculation method the timing of the previous lows.
Additionally, the user can choose to extend this time zone or to limit them to the range between the last pivot high and low.
[blackcat] L2 Fourier Series AnalysisLevel 2
Background
John Ehlers’ articles in the July issues on 2019,“Fourier Series Model Of The Market”.
Function
In “Fourier Series Model Of The Market” in this issue, author John Ehlers introduces a Fourier series indicator designed to help traders identify cycles in the market. According to the author, the approach based on five principles outlined by J.M. Hurst in his 1970 book allows the determinization of a security’s primary cycle period and gives a faithful picture of market activity.
Remarks
You have to adjust Entry_TH value for different time frames.
Feedbacks are appreciated.
Rescaled RangeRescaled Range is an implementation of the fractal rescaled ranges developed by Harold Edwin Hurst and Benoit Mandlebrot.
Settings include:
“Window Size” - the number of time periods in a window over which price changes are analyzed. This will generally correspond to your trading horizon and defaults to 15.
“Number of Windows” - the number of “Window Size” intervals to average the rescaled range value over. By looking at a number of such periods, the study captures potential volatility that may have occurred in the recent past. This should be set long enough to capture the current trend (defaults to 63), but not so long to include volatility regimes no longer in play.
Each window in the average is offset by 1 time period from the the others - like a moving average.
This study plots two lines - “Rescaled Range High” which indicates overbought conditions when the price moves above it and “Rescaled Range Low” which indicates oversold conditions when the price moves below it.
This study builds upon the bridge range work of Joe Catanzaro (joecat808) and Caleb Sandfort (calebsandfort). Bridge ranges are used to position the rescaled range with respect to the closing price.
Note: Your time series must have (Window Size + Number of Windows) or more periods of data to complete this study. For example, using the defaults, your time series should have (15+63) = 78 periods or more of data.
