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.
- 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:
- Calculate the mean of the price series
- Create a mean-adjusted series by subtracting the mean from each value
- Calculate the cumulative deviation from the mean
- Compute the range (R) as max cumulative deviation minus min cumulative deviation
- Divide by the standard deviation (S) to get the rescaled range
- The Hurst Exponent is derived from how R/S scales with time
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.
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.
Further Reading
Foundational papers
- Hurst, H. E. (1951). Long-term Storage Capacity of Reservoirs. Transactions of the American Society of Civil Engineers, 116, 770–799.
- Lo, A. W. (1991). Long-term Memory in Stock Market Prices. Econometrica, 59(5), 1279–1313.
Textbook references
- Campbell, J. Y., Lo, A. W. & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press.
- Tsay, R. S. (2010). Analysis of Financial Time Series (3rd ed.). Wiley.
Related QuanterLab articles
Try it in QuanterLab
Compute Hurst on a known mean-reverter (e.g., a sector-index spread) and a known trender (e.g., a momentum leader). The contrast between < 0.45 and > 0.55 gives you intuition for what tradable mean-reversion looks like statistically.