Interpreting the Hurst Exponent as Long-Range Dependence
Summary
The Hurst exponent describes how strongly observations in a time series remain related across long lags. The document explains its origins in hydrology, where it was developed to study long-run variation in river flow, and connects it to the decay of autocorrelation as the gap between observations grows. For traders and researchers, it offers a way to characterize whether a series tends to persist in one direction or alternate between high and low values.
Values above 0.5 are associated with persistent behavior, while values below 0.5 indicate long-lived alternation. A value of 0.5 is consistent with uncorrelated data, but can also describe series with short-lag correlations that fade exponentially. The note provides conceptual interpretation rather than an estimation procedure, trading rule, or empirical market test. It does not establish that a particular Hurst value predicts returns or remains stable across assets and periods.
Key ideas
- The Hurst exponent summarizes long-range dependence in a time series.
- Values above 0.5 indicate a tendency for observations to persist in the same direction.
- Values below 0.5 indicate a tendency for high and low observations to alternate.
- A value of 0.5 can reflect uncorrelated data or quickly decaying short-lag autocorrelation.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.