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Article Dans Une Revue Annals of Statistics Année : 2007

Estimation of the Hurst parameter from discrete noisy data

Marc Hoffmann
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Résumé

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.

Dates et versions

hal-00693086 , version 1 (01-05-2012)

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Citer

Arnaud Gloter, Marc Hoffmann. Estimation of the Hurst parameter from discrete noisy data. Annals of Statistics, 2007, 35 (5), pp.1947--1974. ⟨10.1214/009053607000000316⟩. ⟨hal-00693086⟩
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