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Estimation of the Hurst parameter from discrete noisy data

Abstract : We estimate the Hurst parameter H of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of H more difficult since relevant information is mostly contained in the high frequencies of the signal. We quantify the difficulty of the statistical problem in a min-max sense: we prove that the rate n(-1/(4H+2)) is optimal for estimating H and propose rate optimal estimators based on adaptive estimation of quadratic functionals.
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Submitted on : Tuesday, May 1, 2012 - 8:04:13 PM
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Arnaud Gloter, Marc Hoffmann. Estimation of the Hurst parameter from discrete noisy data. Annals of Statistics, Institute of Mathematical Statistics, 2007, 35 (5), pp.1947--1974. ⟨10.1214/009053607000000316⟩. ⟨hal-00693086⟩



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