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October 2007 Estimation of the Hurst parameter from discrete noisy data
Arnaud Gloter, Marc Hoffmann
Ann. Statist. 35(5): 1947-1974 (October 2007). DOI: 10.1214/009053607000000316


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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Arnaud Gloter. Marc Hoffmann. "Estimation of the Hurst parameter from discrete noisy data." Ann. Statist. 35 (5) 1947 - 1974, October 2007.


Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62073
MathSciNet: MR2363959
Digital Object Identifier: 10.1214/009053607000000316

Primary: 60G18 , 62F12 , 62G99 , 62M09

Keywords: adaptive estimation of quadratic functionals , fractional Brownian motion , High frequency data , noisy data , Scaling exponent , Wavelet methods

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 5 • October 2007
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