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arXiv · 0910.3088

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

Jean-Christophe Breton·Jean-François Coeurjolly
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Abstract

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 $H$.

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Jean-Christophe Breton, Jean-François Coeurjolly. 2010-05-31. Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size. https://arxiv.org/abs/0910.3088

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