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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 (8)
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

Minor changes.

31 Jan 2013

minor changes

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