Hurst Exponent: Regime Detection

The Hurst Exponent is a statistical measure used to classify time series as trending, mean-reverting, or random. Named after hydrologist Harold Edwin Hurst, this metric has become a cornerstone of quantitative mean reversion analysis.

What the Hurst Exponent Measures

The Hurst Exponent (H) measures the long-term memory of a time series—specifically, how strongly past values influence future values. It provides a single number between 0 and 1 that characterizes the behavior of price movements.

Hurst Exponent Interpretation
  • H < 0.5 - Mean-reverting: past increases tend to be followed by decreases
  • H = 0.5 - Random walk: no predictable pattern (like a coin flip)
  • H > 0.5 - Trending: past increases tend to be followed by more increases

Calculation Method: Rescaled Range Analysis

QuanterLab calculates the Hurst Exponent using Rescaled Range (R/S) analysis over a 100-bar lookback period. The process involves:

  1. Calculate the mean of the price series
  2. Create a mean-adjusted series by subtracting the mean from each value
  3. Calculate the cumulative deviation from the mean
  4. Compute the range (R) as max cumulative deviation minus min cumulative deviation
  5. Divide by the standard deviation (S) to get the rescaled range
  6. The Hurst Exponent is derived from how R/S scales with time
R/S ~ (n)^H where H is the Hurst Exponent

Platform Scoring

The platform converts the raw Hurst Exponent into a 0-100 score for easy comparison:

  • H ≤ 0.3 - Score: 100 (strong mean reversion)
  • H = 0.5 - Score: 50 (neutral/random walk)
  • H ≥ 0.7 - Score: 0 (strong trending, not suitable)

Securities must achieve a minimum composite score that includes the Hurst component to appear in scanner results.

Why Hurst Matters for Mean Reversion

A stock might appear oversold based on RSI or Bollinger Bands, but if its Hurst Exponent indicates trending behavior (H > 0.5), mean reversion strategies are statistically less likely to succeed. The Hurst Exponent acts as a regime filter, helping identify when mean reversion is a reasonable expectation.

Key Insight

The Hurst Exponent answers the question: "Is this security exhibiting mean-reverting behavior?" Only after confirming mean-reverting characteristics does it make sense to look for entry signals.

Limitations

  • The Hurst Exponent is backward-looking and regimes can change
  • Results depend on the lookback period chosen
  • During transitions between regimes, readings may be unreliable

This is why the platform uses Hurst as one component of a multi-factor scoring system rather than relying on it alone.

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