Estimation of the Hurst parameter from discrete noisy data
The Annals of Statistics · 2007 · Volume 35 · Issue 5
DOI: 10.1214/009053607000000316
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.
Keywords
60G18, 62F12, 62G99, 62M09, adaptive estimation of quadratic functionals, fractional Brownian motion, High frequency data, noisy data, Scaling exponent, Wavelet methods
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