The Annals of Statistics

Estimation of the Hurst parameter from discrete noisy data

Arnaud Gloter and Marc Hoffmann

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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.

Article information

Ann. Statist., Volume 35, Number 5 (2007), 1947-1974.

First available in Project Euclid: 7 November 2007

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Zentralblatt MATH identifier

Primary: 60G18: Self-similar processes 62G99: None of the above, but in this section 62F12: Asymptotic properties of estimators 62M09: Non-Markovian processes: estimation

Scaling exponent noisy data high frequency data fractional Brownian motion adaptive estimation of quadratic functionals wavelet methods


Gloter, Arnaud; Hoffmann, Marc. Estimation of the Hurst parameter from discrete noisy data. Ann. Statist. 35 (2007), no. 5, 1947--1974. doi:10.1214/009053607000000316.

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