Hurstexponent — 指標和策略

Hurst Exponent Oscillator [PhenLabs]📊 Hurst Exponent Oscillator - Version: PineScript™ v5 📌 Description The Hurst Exponent Oscillator (HEO) by PhenLabs is a powerful tool developed for traders who want to distinguish between trending, mean-reverting, and random market behaviors with clarity and precision. By estimating the Hurst Exponent—a statistical measure of long-term memory in financial time series—this indicator helps users make sense of underlying market dynamics that are often not visible through traditional moving averages or oscillators. Traders can quickly know if the market is likely to continue its current direction (trending), revert to the mean, or behave randomly, allowing for more strategic timing of entries and exits. With customizable smoothing and clear visual cues, the HEO enhances decision-making in a wide range of trading environments. 🚀 Points of Innovation Integrates advanced Hurst Exponent calculation via Rescaled Range (R/S) analysis, providing unique market character insights. Offers real-time visual cues for trending, mean-reverting, or random price action zones. User-controllable EMA smoothing reduces noise for clearer interpretation. Dynamic coloring and fill for immediate visual categorization of market regime. Configurable visual thresholds for critical Hurst levels (e.g., 0.4, 0.5, 0.6). Fully customizable appearance settings to fit different charting preferences. 🔧 Core Components Log Returns Calculation: Computes log returns of the selected price source to feed into the Hurst calculation, ensuring robust and scale-independent analysis. Rescaled Range (R/S) Analysis: Assesses the dispersion and cumulative deviation over a rolling window, forming the core statistical basis for the Hurst exponent estimate. Smoothing Engine: Applies Exponential Moving Average (EMA) smoothing to the raw Hurst value for enhanced clarity. Dynamic Rolling Windows: Utilizes arrays to maintain efficient, real-time calculations over user-defined lengths. Adaptive Color Logic: Assigns different highlight and fill colors based on the current Hurst value zone. 🔥 Key Features Visually differentiates between trending, mean-reverting, and random market modes. User-adjustable lookback and smoothing periods for tailored sensitivity. Distinct fill and line styles for each regime to avoid ambiguity. On-chart reference lines for strong trending and mean-reverting thresholds. Works with any price series (close, open, HL2, etc.) for versatile application. 🎨 Visualization Hurst Exponent Curve: Primary plotted line (smoothed if EMA is used) reflects the ongoing estimate of the Hurst exponent. Colored Zone Filling: The area between the Hurst line and the 0.5 reference line is filled, with color and opacity dynamically indicating the current market regime. Reference Lines: Dash/dot lines mark standard Hurst thresholds (0.4, 0.5, 0.6) to contextualize the current regime. All visual elements can be customized for thickness, color intensity, and opacity for user preference. 📖 Usage Guidelines Data Settings Hurst Calculation Length Default: 100 Range: 10-300 Description: Number of bars used in Hurst calculation; higher values mean longer-term analysis, lower values for quicker reaction. Data Source Default: close Description: Select which data series to analyze (e.g., Close, Open, HL2). Smoothing Length (EMA) Default: 5 Range: 1-50 Description: Length for smoothing the Hurst value; higher settings yield smoother but less responsive results. Style Settings Trending Color (Hurst > 0.5) Default: Blue tone Description: Color used when trending regime is detected. Mean-Reverting Color (Hurst < 0.5) Default: Orange tone Description: Color used when mean-reverting regime is detected. Neutral/Random Color Default: Soft blue Description: Color when market behavior is indeterminate or shifting. Fill Opacity Default: 70-80 Range: 0-100 Description: Transparency of area fills—higher opacity for stronger visual effect. Line Width Default: 2 Range: 1-5 Description: Thickness of the main indicator curve. ✅ Best Use Cases Identifying if a market is regime-shifting from trending to mean-reverting (or vice versa). Filtering signals in automated or systematic trading strategies. Spotting periods of randomness where trading signals should be deprioritized. Enhancing mean-reversion or trend-following models with regime-awareness. ⚠️ Limitations Not predictive: Reflects current and recent market state, not future direction. Sensitive to input parameters—overfitting may occur if settings are changed too frequently. Smoothing can introduce lag in regime recognition. May not work optimally in markets with structural breaks or extreme volatility. 💡 What Makes This Unique Employs advanced statistical market analysis (Hurst exponent) rarely found in standard toolkits. Offers immediate regime visualization through smart dynamic coloring and zone fills. 🔬 How It Works Rolling Log Return Calculation: Each new price creates a log return, forming the basis for robust, non-linear analysis. This ensures all price differences are treated proportionally. Rescaled Range Analysis: A rolling window maintains cumulative deviations and computes the statistical “range” (max-min of deviations). This is compared against the standard deviation to estimate “memory”. Exponent Calculation & Smoothing: The raw Hurst value is translated from the log of the rescaled range ratio, and then optionally smoothed via EMA to dampen noise and false signals. Regime Detection Logic: The smoothed value is checked against 0.5. Values above = trending; below = mean-reverting; near 0.5 = random. These control plot/fill color and zone display. 💡 Note: Use longer calculation lengths for major market character study, and shorter ones for tactical, short-term adaptation. Smoothing balances noise vs. lag—find a best fit for your trading style. Always combine regime awareness with broader technical/fundamental context for best results.

Advanced Fractal and Hurst Indicator Advanced Fractal and Hurst Indicator (AFHI) Description: The Advanced Fractal and Hurst Indicator (AFHI) is a custom technical analysis tool designed to identify market trends and potential reversals by leveraging the concepts of Fractal Dimension and the Hurst Exponent . These advanced mathematical concepts provide insights into the complexity and persistence of price movements, making this indicator a powerful addition to any trader's toolkit. How It Works: Fractal Dimension (FD) : The Fractal Dimension measures the complexity of price movements. A higher Fractal Dimension indicates a more complex, choppy market, while a lower value suggests smoother trends. The FD is calculated using the log difference of price movements over a specified length. Hurst Exponent (HE) : The Hurst Exponent indicates the tendency of a time series to either regress to the mean or cluster in a direction. Values below 0.5 indicate a tendency to revert to the mean (mean-reverting), while values above 0.5 suggest a trending market. The HE is calculated using the rescaled range method, comparing the range of price movements to the standard deviation. Composite Indicator : The Composite Indicator combines the smoothed Fractal Dimension and Hurst Exponent to provide a single value indicating market conditions. This is done by normalizing the FD and HE values and combining them into one metric. A positive Composite Indicator suggests an uptrend, while a negative value indicates a downtrend. Smoothing : Both FD and HE values are smoothed using a simple moving average to reduce noise and provide clearer signals. Trend Confirmation : A 50-period moving average (MA) is used to confirm the trend direction. The price being above the MA indicates an uptrend, while below the MA indicates a downtrend. Background Shading : The indicator pane is shaded green during uptrend conditions (positive Composite Indicator and price above MA) and red during downtrend conditions (negative Composite Indicator and price below MA). How Traders Can Use It: Identifying Trends : Traders can use the AFHI to identify current market trends. The background shading in the indicator pane provides a visual cue for trend direction, with green indicating an uptrend and red indicating a downtrend. Trend Confirmation : The Composite Indicator line, plotted in purple, helps confirm the trend. Positive values suggest a strong uptrend, while negative values indicate a strong downtrend. Entry and Exit Signals : Traders can use the transitions of the Composite Indicator and the background shading to time their entry and exit points. For instance, a shift from red to green shading suggests a potential buy opportunity, while a shift from green to red suggests a potential sell opportunity. Alerts : The script includes alert conditions that can notify traders when the Composite Indicator signals a new trend direction. Alerts can be set up for both uptrends and downtrends, helping traders stay informed of key market changes. Strategy Development : By integrating AFHI into their trading strategies, traders can develop more robust systems that account for market complexity and persistence. The indicator can be used alongside other technical tools to enhance decision-making and improve trade accuracy.

Hurst Exponent (Dubuc's variation method)Library "Hurst" hurst(length, samples, hi, lo) Estimate the Hurst Exponent using Dubuc's variation method Parameters: length : The length of the history window to use. Large values do not cause lag. samples : The number of scale samples to take within the window. These samples are then used for regression. The minimum value is 2 but 3+ is recommended. Large values give more accurate results but suffer from a performance penalty. hi : The high value of the series to analyze. lo : The low value of the series to analyze. The Hurst Exponent is a measure of fractal dimension, and in the context of time series it may be interpreted as indicating a mean-reverting market if the value is below 0.5 or a trending market if the value is above 0.5. A value of exactly 0.5 corresponds to a random walk. There are many definitions of fractal dimension and many methods for its estimation. Approaches relying on calculation of an area, such as the Box Counting Method, are inappropriate for time series data, because the units of the x-axis (time) do match the units of the y-axis (price). Other approaches such as Detrended Fluctuation Analysis are useful for nonstationary time series but are not exactly equivalent to the Hurst Exponent. This library implements Dubuc's variation method for estimating the Hurst Exponent. The technique is insensitive to x-axis units and is therefore useful for time series. It will give slightly different results to DFA, and the two methods should be compared to see which estimator fits your trading objectives best. Original Paper: Dubuc B, Quiniou JF, Roques-Carmes C, Tricot C. Evaluating the fractal dimension of profiles. Physical Review A. 1989;39(3):1500-1512. DOI: 10.1103/PhysRevA.39.1500 Review of various Hurst Exponent estimators for time-series data, including Dubuc's method: www.intechopen.com

HurstExponent Library "HurstExponent" Library to calculate Hurst Exponent refactored from Hurst Exponent - Detrended Fluctuation Analysis demean(src) Calculates a series subtracted from the series mean. Parameters: src : The series used to calculate the difference from the mean (e.g. log returns). Returns: The series subtracted from the series mean cumsum(src, length) Calculates a cumulated sum from the series. Parameters: src : The series used to calculate the cumulative sum (e.g. demeaned log returns). length : The length used to calculate the cumulative sum (e.g. 100). Returns: The cumulative sum of the series as an array aproximateLogScale(scale, length) Calculates an aproximated log scale. Used to save sample size Parameters: scale : The scale to aproximate. length : The length used to aproximate the expected scale. Returns: The aproximated log scale of the value rootMeanSum(cumulativeSum, barId, numberOfSegments) Calculates linear trend to determine error between linear trend and cumulative sum Parameters: cumulativeSum : The cumulative sum array to regress. barId : The barId for the slice numberOfSegments : The total number of segments used for the regression calculation Returns: The error between linear trend and cumulative sum averageRootMeanSum(cumulativeSum, barId, length) Calculates the Root Mean Sum Measured for each block (e.g the aproximated log scale) Parameters: cumulativeSum : The cumulative sum array to regress and determine the average of. barId : The barId for the slice length : The length used for finding the average Returns: The average root mean sum error of the cumulativeSum criticalValues(length) Calculates the critical values for a hurst exponent for a given length Parameters: length : The length used for finding the average Returns: The critical value, upper critical value and lower critical value for a hurst exponent slope(cumulativeSum, length) Calculates the hurst exponent slope measured from root mean sum, scaled to log log plot using linear regression Parameters: cumulativeSum : The cumulative sum array to regress and determine the average of. length : The length used for the hurst exponent sample size Returns: The slope of the hurst exponent smooth(src, length) Smooths input using advanced linear regression Parameters: src : The series to smooth (e.g. hurst exponent slope) length : The length used to smooth Returns: The src smoothed according to the given length exponent(src, hurstLength) Wrapper function to calculate the hurst exponent slope Parameters: src : The series used for returns calculation (e.g. close) hurstLength : The length used to calculate the hurst exponent (should be greater than 50) Returns: The src smoothed according to the given length

Hurst Exponent My first try to implement Full Hurst Exponent. The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series and the rate at which these decrease as the lag between pairs of values increases The Hurst exponent is referred to as the "index of dependence" or "index of long-range dependence". It quantifies the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction. In short, depending on the value you can spot the trending / reversing market. Values 0.5 to 1 - market trending Values 0 to 0.5 - market tend to mean revert Hurst Exponent is computed using Rescaled range (R/S) analysis. I split the lookback period (N) in the number of shorter samples (for ex. N/2, N/4, N/8, etc.). Then I calculate rescaled range for each sample size. The Hurst exponent is estimated by fitting the power law. Basically finding the slope of log(samples_size) to log(RS). You can choose lookback and sample sizes yourself. Max 8 possible at the moment, if you want to use less use 0 in inputs. It's pretty computational intensive, so I added an input so you can limit from what date you want it to be calculated. If you hit the time limit in PineScript - limit the history you're using for calculations. #################### Disclaimer Please remember that past performance may not be indicative of future results. Due to various factors, including changing market conditions, the strategy may no longer perform as good as in historical backtesting. This post and the script don’t provide any financial advice.

Simple Hurst Exponent [QuantNomad]This is a simplified version of the Hurst Exponent indicator. In the meantime, I'm working on the full version. It's computationally intensive, so it's a challenge to squeeze it to PineScript limits. It will require some time to optimize it, so I decided to publish a simplified version for now. The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases The Hurst exponent is referred to as the "index of dependence" or "index of long-range dependence". It quantifies the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction. In short depend on value you can spot trending / reversing market. Values 0.5 to 1 - market trending Values 0 to 0.5 - market tend to mean revert #################### Disclaimer Please remember that past performance may not be indicative of future results. Due to various factors, including changing market conditions, the strategy may no longer perform as good as in historical backtesting. This post and the script don’t provide any financial advice.

[NLX-L2] Hurst Exponent Signal Filter - Hurst Exponent Signal Filter - The Hurst Exponent Signal Filter is meant to be used with an external signal source, this can be any indicator with a signal plot output (-1 Sell / 1 Buy) It filters out a lot of noisy signals and improves the performance of many indicators. - Example: How to Use - 1. Add a trend Indicator like Trend Index MTF to your chart 2. Add an indicator with a signal plot like Fishers Stochastic Center of Gravity to your Chart and select the Trend Index MTF with Type L1 in the Settings as Signal Source 3. Add this Hurst Signal Filter to your Chart and select the Fishers Stochastic Center of Gravity with Type L2 in the Settings as Signal Source 4. Add the Backtest Module to your Chart and select the Hurst Signal Filter with Type L2 as Source - Alerts for Automated Trading - See my signature below. Contact me for the Alert module.