Abstract:
Sample statistics of samples from a fractional Brownian motion with Hurst exponent $H$, and in particular, autocovariance statistics, are considered. Two statistics characterizing the covariate dependence between the increments of this process are studied; in particular, their asymptotic properties and the limit distributions are examined. Each of the statistics is shown to converge almost everywhere; their limits are evaluated. It is found that these statistics have different limit distributions depending on the value of $H$. A complete description of these distributions in terms of semi-invariants is put forward.
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