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I am looking for the Hurst exponent calculation methodology. Please suggest online materials / methodology papers.

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The calculation is covered on the related wikipedia page.

R has several implementations for this:

  1. The fArma package provides 10 different functions to estimate the Hurst exponent (see LrdModelling).
  2. The Rwave package has the hurst.est() function.
  3. The fractal package has the hurstACVF() function.
  4. The dvfBm package is intended entirely for this purpose: "Hurst exponent estimation of a fractional Brownian motion by using discrete variations methods in presence of outliers and/or an additive noise".

The methods covered by fArma are taken from the "Estimators for Long-Range Dependence: An Empirical Study" (Taqqu, Teverovsky, Willinger 1995).

Edit: Just to add from the M. Tibbits comment below, you can find the Hurst exponent code for Matlab offered under a BSD license. The description:

This is an implementation of the Hurst exponent calculation that is smaller, simpler, and quicker than most others. It does a dispersional analysis on the data and then uses Matlab's polyfit to estimate the Hurst exponent. It comes with a test driver that you can delete.

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  • $\begingroup$ Thank you! Do you know any Matlab / Mathematica based packages? $\endgroup$ – Eduardas Oct 8 '10 at 14:12
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    $\begingroup$ No, I'm afraid not. But R is fully open source so all the algorithms above will be very transparent if you want to re-implement. $\endgroup$ – Shane Oct 8 '10 at 14:20
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    $\begingroup$ and if you google for matlab hurst exponent you'll find several. $\endgroup$ – PeterR Oct 8 '10 at 14:42
  • $\begingroup$ First result from google: Hurst Exponential $\endgroup$ – M. Tibbits Oct 8 '10 at 14:59
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Octave has a built-in Hurst Exponent function.

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