Indicators Description

1. Component Deconstruction¶

A. Hurst Exponent (Custom Implementation)¶

This is the strategic core of the script, implemented via a custom variance scaling method rather than a built-in function.

• Specific Configuration:

  • Lookback Period (active_h_period): Default is 60 bars. This defines the window for variance calculations.

  • Scaling Lag (active_h_lag): Default is 10 bars. This is the q in the variance ratio, representing the longer-term return horizon.

  • Price Source: close price is used exclusively for all calculations.

• Functional Modification:

  • The script calculates the Hurst exponent H by comparing the variance of 1-period returns to the variance of q-period returns over a p-bar lookback window.

  • Mathematical Logic:

    1. var1 = ta.variance(close - close[1], active_h_period): Calculates the variance of single-period price changes. This represents short-term, high-frequency price fluctuation.

    2. varq = ta.variance(close - close[active_h_lag], active_h_period): Calculates the variance of q-period price changes. This represents longer-term price fluctuation.

    3. H_raw = math.log(varq / var1) / (2.0 * math.log(active_h_lag)): This is the variance-scaling formula. H is derived from the logarithmic relationship between the ratio of long-term to short-term variance and the scaling lag q.

    4. H = math.max(0.0, math.min(H_raw, 1.0)): The raw H value is clamped between 0.0 and 1.0 to maintain theoretical bounds and prevent calculation errors from extreme market data.

    5. safeH = nz(H, 0.5): A “safe” version of H is created. If H is na (during the initial bars of the chart), it defaults to 0.5, representing a neutral, random-walk assumption.

B. Kalman Filter (Custom, 1-D)¶

This acts as the script’s primary signal line, replacing a traditional moving average to reduce lag while smoothing price.

• Specific Configuration:

  • Base Tracking Gain (active_kf_gain): Default is 0.2. This is the baseline smoothing factor before adaptation.

  • Price Source: The filter is applied directly to the close price.

• Functional Modification:

  • The script employs a non-standard, adaptive Kalman Filter where the tracking gain is dynamically modulated by the Hurst exponent.

  • Mathematical Logic:

    1. adaptive_gain = active_kf_gain * (0.5 + safeH): The tracking gain is not static. It is scaled by a factor derived from the Hurst exponent.

       • Trending Market (H -> 1.0): adaptive_gain approaches active_kf_gain * 1.5. The filter becomes more sensitive and tracks price more aggressively, reducing lag.

       • Mean-Reverting Market (H -> 0.0): adaptive_gain approaches active_kf_gain * 0.5. The filter becomes less sensitive and provides more smoothing, ignoring noise.

       • Random Walk Market (H = 0.5): adaptive_gain equals active_kf_gain * 1.0. The filter operates at its base configuration.

    2. kf := kf[1] + adaptive_gain * (close - kf[1]): This is the recursive update formula for a simple one-dimensional Kalman filter (or more accurately, an Exponential Moving Average with a dynamic alpha). The new filter value is the previous value plus a fraction (the adaptive_gain) of the error between the current price and the previous filter value.

C. Average True Range (ATR)¶

This component provides the raw volatility measurement used to calculate the band width.

• Specific Configuration:

  • Length (active_atr_len): Default is 10 periods.

  • Source: Standard high, low, and close prices via the ta.atr() function.

• Functional Modification:

  • The ATR value itself is standard. Its modification occurs in how it is multiplied and applied in the Supertrend framework.

D. Supertrend Framework (Custom, Adaptive)¶

This structure provides the dynamic upper and lower bands that serve as the trigger levels.

• Specific Configuration:

  • Signal Line: The Kalman Filtered price (kf) is used as the central pivot, not the close price.

  • Base Multiplier (active_atr_base): Default is 1.5. This sets the minimum possible band width in ATR units.

  • Hurst Scale Factor (active_atr_hscale): Default is 3.0. This controls the magnitude of band widening in low-Hurst regimes.

• Functional Modification:

  • This is a heavily modified Supertrend where the ATR multiplier is not a fixed constant but a dynamic variable controlled by the Hurst exponent.

  • Mathematical Logic:

    1. h_mult = active_atr_base + active_atr_hscale * (1.0 - safeH): This formula calculates the dynamic ATR multiplier.

       • Strong Trend (H -> 1.0): The term (1.0 - safeH) approaches 0. The multiplier h_mult collapses to its minimum value, active_atr_base. This results in tighter bands for more responsive entries and exits.

       • Strong Mean-Reversion (H -> 0.0): The term (1.0 - safeH) approaches 1. The multiplier h_mult expands to its maximum value, active_atr_base + active_atr_hscale. This results in significantly wider bands to filter out whipsaws in choppy markets.

    2. band = ta.atr(active_atr_len) * h_mult: The final band offset is the product of the standard ATR and this Hurst-adaptive multiplier.

    3. The core Supertrend logic (upBand, dnBand, trend) is then applied using the Kalman Filter (kf) as the price source and this dynamic band offset.

2. Logic Layering & Confluence¶

The script’s engine is built on a strict hierarchical filtering model, where each layer processes information from the layer above it, progressively refining the signal and reducing noise.

• Hierarchical Filtering:

  1. Primary Layer (Regime Diagnosis): The Hurst Exponent acts as the master “Gatekeeper.” It does not generate signals but provides a single, quantitative measure of the market’s character (trending, random, or mean-reverting). All subsequent calculations are subordinate to its output.

  2. Secondary Layer (Signal Processing): The Kalman Filter takes the raw close price and smooths it. Its behavior is directly governed by the Hurst Exponent from the primary layer. It becomes a “regime-aware” signal line, lagging less in trends and smoothing more in chop.

  3. Tertiary Layer (Trigger Definition): The Adaptive Supertrend Bands form the final filter. Their distance from the Kalman Filter signal line is also governed by the Hurst Exponent. They use the processed output from the secondary layer (kf) as their central axis.

• Interaction Dynamics:

  • The system is fundamentally based on Confluence. A trade signal is only generated when the market regime (Hurst), smoothed momentum (Kalman), and volatility-based price action (Supertrend cross) align.

  • The core interaction is a Threshold Cross. The trigger is the Kalman Filter (kf) crossing one of the adaptive Supertrend bands. However, the thresholds themselves are dynamic, constantly being adjusted by the Hurst exponent, making it a “smart” threshold system.

3. The Execution Engine¶

The final signal is the result of a clear boolean state machine based on the interaction between the Kalman Filter and the adaptive bands.

• Boolean Logic:

  • Trend State (trend): A state variable (trend) holds the current market direction (1 for Bullish, -1 for Bearish).

  • Bullish Trigger (turnedBullish): This becomes true on the single bar where the trend flips from bearish to bullish. The condition for this flip is kf > prevDn (the Kalman Filter crosses above the previous period’s lower band).

  • Bearish Trigger (turnedBearish): This becomes true on the single bar where the trend flips from bullish to bearish. The condition for this flip is kf < prevUp (the Kalman Filter crosses below the previous period’s upper band).

  • Exit Logic: The system operates on a “flip-and-reverse” basis. The trigger for a new bullish trend is simultaneously the exit signal for a bearish trend, and vice versa.

• Mathematical Constants:

  • active_atr_base (Default: 1.5): This is a critical risk-management constant. It establishes a minimum risk floor. It ensures that even in a perfectly trending market (H=1.0), the stop-loss level (the band) is at least 1.5 ATRs away from the Kalman Filter line, preventing excessively tight stops that are prone to noise.

  • active_atr_hscale (Default: 3.0): This constant dictates the defensive posture of the strategy. It controls how aggressively the bands widen in choppy markets. A higher value means the system will require a much larger volatility-adjusted price move to trigger a signal when the Hurst exponent is low, significantly increasing its immunity to whipsaws.

  • 0.5 in (0.5 + safeH): This is a centering constant for the Kalman gain. It ensures that in a perfectly random market (H=0.5), the adaptive gain multiplier is exactly 1.0, causing the filter to operate at its user-defined base gain.

  • 1.0 in (1.0 - safeH): This is an inversion constant for the band multiplier. It translates a high Hurst value (trending) into a low multiplier and a low Hurst value (choppy) into a high multiplier, achieving the desired adaptive behavior.