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Generalized Hurst exponent

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Generalized Hurst exponent



18 Jan 2011 (Updated )

Generalized Hurst exponent of a stochastic variable

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Calculates the generalized Hurst exponent H(q) of a stochastic variable x(t) (a time series) from the scaling of the renormalized q-moments of the distribution

<|x(t+r)-x(t)|^q>/<x(t)^q> ~ r^[qH(q)]

The value of H(q) give indication about the fractal nature of the signal. H(q) = 0.5 corresponds to a Brownian motion, deviations form 0.5 and dependency on q are indications of multi-fractality and time-correlations.

MATLAB release MATLAB 7.12 (R2011a)
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Comments and Ratings (12)
31 Dec 2016 roger wang

30 Jun 2016 Jiayi XIE

16 Sep 2015 Milot

Milot (view profile)

10 Sep 2015 igor skachkov

a little biased on a pure random walk. is it possible to add corrections/

16 Dec 2013 BOJING ZHU


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01 Nov 2013 Thomas

Thomas (view profile)

30 Jul 2013 xinxing

17 Jan 2013 Tomaso Aste

The Hurst exponent for a random walk is indeed 0.5. The Hurst exponent for a random variable is instead 0. If you apply the genhurst to cumsum(randn) and you will get numbers close to 0.5.

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16 Jan 2013 Sandro

Sandro (view profile)

I tried your file with a random time series (both rand and randn) and this values of obtained is close to 0 (although it should be close to 0.5 right?). Can you explain it?

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07 May 2012 WARR

WARR (view profile)

29 Jan 2012 faruto

faruto (view profile)

26 Jan 2012 Lars

Lars (view profile)

02 May 2012 1.1

Minor changes.

31 Jan 2013 1.2

minor changes

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