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Generalized Hurst exponent

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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.

Comments and Ratings (14)

M T

M T (view profile)

good function. THX

roger wang

Jiayi XIE

Milot

Milot (view profile)

igor skachkov

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

BOJING ZHU

good

Thomas

Thomas (view profile)

xinxing

Tomaso Aste

Tomaso Aste (view profile)

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.

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?

WARR

WARR (view profile)

faruto

faruto (view profile)

Lars

Lars (view profile)

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