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

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

2009-10-16

arxiv.org/abs/0910.3088v2

Mathematics

Statistics Theory

Scientific paper

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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