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Consider a time series of real number $x_1, x_2,\dots,...x_n$. How one can define fractal dimension of this series?

I would like to know famous formula $F+H=2$ where H is Hurst exponent and F is fractal dimension of a one dimensional time series.

http://en.wikipedia.org/wiki/Hurst_exponent

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    $\begingroup$ you'll want to calculate the correlation function, Fourier transform it and then the power law decay gives you the fractal dimension; are you looking for software packages that do this for you? $\endgroup$ Mar 31 '15 at 17:51
  • $\begingroup$ Yes. Would you please let me know which software? $\endgroup$ Apr 1 '15 at 2:38
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Scipy.signal has package called 'welch' or 'periodogram' which calculates the power spectra of any given time series with respective methods. Loglog plot of power spectra will give you the exponent of power-law decay (if there is).

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