Hurst Exponent

The Hurst exponent is a statistical measure used to uncover the long-term memory of a time series. It helps determine if a financial asset is purely random (H = 0.5), trending (H > 0.5), or mean-reverting (H < 0.5).

Wiener Process

We sample a Wiener process path over one day (one time step per second) and estimate the Hurst exponent from both realized variance and range-based OHLC estimators.

Range-based Volatility Estimators

Volatility estimated from OHLC data using Parkinson (1980), Garman & Klass (1980), and Rogers & Satchell (1991) estimators across different sampling periods.

Mean-Reverting (Vasicek)

For mean-reverting processes, the Hurst exponent is less than 0.5. Higher mean reversion (kappa) leads to a lower Hurst exponent.