Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size |
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| Authors: | Jean-Christophe Breton Jean-Fran?ois Coeurjolly |
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| Institution: | 1. Institut de Recherche Math??matique de Rennes, Universit?? de Rennes 1, Rennes, France
2. GIPSA-Lab and Laboratory Jean Kuntzmann, Grenoble University, Grenoble, France
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| Abstract: | In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose 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 Hurst parameter H. |
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| Keywords: | |
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