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Is there a test in Matlab if a time series satisfies properties of being a fractional Brownian motion?

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    $\begingroup$ Have a look at our help center to see what kinds of questions are considered on-topic here. Finding implementations of a test on a particular statistical platform is outside our scope, but the wider question of how to test for fractional Brownian motion would be on-topic. I think it would be worth editing the question to bring out the underlying statistical point rather than focus on the software implementation. $\endgroup$
    – Silverfish
    Jun 1 '16 at 23:06
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I don't know if there's a direct routine but, there are spectral and chi-square tests for fractional brownian motion that are fairly straightforward to implement. See for example section 3.2 of this: http://www.columbia.edu/~ad3217/fbm/thesis.pdf

Keep in mind that spectral tests don't preclude your signal from having similar spectrum to fractional brownian motion but being something wholly different (although this is a bit esoteric).

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