# Re: [R] Fractional brownian motion

From: RABINOVITCH Peter <Peter.Rabinovitch_at_alcatel-lucent.com>
Date: Wed 10 Jan 2007 - 14:42:00 GMT

You have applied the Hurst parameter estimating function to the fBm, not the fGn as described in the help page for Long Range Dependence Modelling in fSeries.

"The function aggvarFit computes the Hurst exponent from the variance of an aggregated FGN or FARIMA time series process"

Trying perFit(diff(x)) (where x is your fBm series) gives an estimate of the Hurst Exponent as 0.53527922

Dear All;

I have used fbmSim to simulate a fbm sequence, however, when I tried to estimate the Hurst effect, none of the nine procedures gave me an answer close enough to the real value, which is 0.5 (n=1000). So, would you please advice,

1. which is the best method to estimate the H among the 9 mehods, R/S, higuchi or Whittle?
2. how to choose the levels (default=50), minnpts, cutoff values or if there is any other issues to consider? Would you please send your code if you can get the right estimate for the attached dataset?
3. I also simulated multiple sequences, but some of the estimated results have H>1, how would you explain this, and how to correct it.
4. if I have a sample size of 30, what are your suggestions for estimating the hurst effect.

Sincerely;

Qing

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))

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