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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


01 Nov 2013 Thomas  
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.

16 Jan 2013 Sandro

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?

07 May 2012 WARR  
29 Jan 2012 faruto  
26 Jan 2012 Lars  
02 May 2012

Minor changes.

31 Jan 2013

minor changes

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