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Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of a fractional Brownian motion and without any assumption on the parameter $H$.

preprint2010arXivOpen access
Jean-Christophe BretonJean-François Coeurjolly
math.STStatistics Theory
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Jean-Christophe BretonJean-François Coeurjolly

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