Estimation of the Hurst parameter from discrete noisy data
Arnaud Gloter and Marc Hoffmann
Source: Ann. Statist. Volume 35, Number 5 (2007), 1947-1974.
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.
Primary Subjects: 60G18, 62G99, 62F12, 62M09
Keywords: Scaling exponent; noisy data; high frequency data; fractional Brownian motion; adaptive estimation of quadratic functionals; wavelet methods
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1194461718
Digital Object Identifier: doi:10.1214/009053607000000316
Mathematical Reviews number (MathSciNet):
MR2363959
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