Estimating the Hurst Exponent with Rescaled-Range Analysis
Summary
The indicator estimates the Hurst exponent from price returns using rescaled-range analysis. For each selected sample length, it divides a rolling lookback into groups, calculates each group’s cumulative-deviation range relative to its standard deviation, and averages those rescaled ranges. It then fits a slope to the logarithms of sample lengths and average rescaled ranges. An optional exponential moving average smooths the plotted estimate, and inputs control the lookback, up to eight sample sizes, smoothing, and the starting date for calculation.
The accompanying explanation interprets values above 0.5 as persistence or trending behavior and values below 0.5 as mean-reverting behavior. This is a regime diagnostic, not a demonstrated trading system: the document reports no predictive or profitability tests. The author describes the implementation as an initial attempt and notes its computational cost; estimates can also depend on the selected samples and lookback, so the interpretation should be validated for the data and horizon being studied.
Key ideas
- The indicator estimates the Hurst exponent by fitting a log-log slope to rescaled ranges across sample sizes.
- It computes returns, partitions the lookback into groups, and normalizes cumulative-deviation ranges by group standard deviation.
- The accompanying interpretation associates estimates above 0.5 with persistence and those below 0.5 with mean reversion.
- Lookback, sample lengths, smoothing, and calculation start date are configurable, but the calculation can be computationally intensive.
- The document provides no evidence that the indicator alone predicts profitable trades.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.