Hurst Exponent (Dubuc's variation method)

Library "Hurst"

hurst(length, samples, hi, lo)
  Estimate the Hurst Exponent using Dubuc's variation method
  Parameters:
    length: The length of the history window to use. Large values do not cause lag.
    samples: The number of scale samples to take within the window. These samples are then used for regression. The minimum value is 2 but 3+ is recommended. Large values give more accurate results but suffer from a performance penalty.
    hi: The high value of the series to analyze.
    lo: The low value of the series to analyze.

The Hurst Exponent is a measure of fractal dimension, and in the context of time series it may be interpreted as indicating a mean-reverting market if the value is below 0.5 or a trending market if the value is above 0.5. A value of exactly 0.5 corresponds to a random walk.

There are many definitions of fractal dimension and many methods for its estimation. Approaches relying on calculation of an area, such as the Box Counting Method, are inappropriate for time series data, because the units of the x-axis (time) do match the units of the y-axis (price). Other approaches such as Detrended Fluctuation Analysis are useful for nonstationary time series but are not exactly equivalent to the Hurst Exponent.

This library implements Dubuc's variation method for estimating the Hurst Exponent. The technique is insensitive to x-axis units and is therefore useful for time series. It will give slightly different results to DFA, and the two methods should be compared to see which estimator fits your trading objectives best.

Original Paper:
Dubuc B, Quiniou JF, Roques-Carmes C, Tricot C. Evaluating the fractal dimension of profiles. Physical Review A. 1989;39(3):1500-1512. DOI: 10.1103/PhysRevA.39.1500

Review of various Hurst Exponent estimators for time-series data, including Dubuc's method:
intechopen.com/chapters/64463