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Given a time series (real data), how can I check if this time series is a fractional brownian motion? I mean, I would start to check for stationary increments. Is it enough to do exploratory plots? Is there any test around, e.h. H0: this stochastic process is a fractional brownian motion?

steffi
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    Fractional Brownian motion doesn't have independent increments. – Nate Eldredge Apr 10 '13 at 13:16
  • you are right, i was confused. – steffi Apr 10 '13 at 13:37
  • I think there are a number of different tests, and their reliability may be hard to evaluate when you're dealing with real-world data. Possibly relevant: http://wiki.cbr.washington.edu/qerm/sites/qerm/images/9/9f/GurarieDissertationFinalDraft.pdf http://iopscience.iop.org/article/10.1088/1742-6596/475/1/012002/pdf https://arxiv.org/abs/1105.4718 You can estimate a Hurst exponent, find how fast the power spectrum falls off, ... –  Jan 30 '17 at 21:48

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