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.
Publié le : 2007-10-14
Classification:
Scaling exponent,
noisy data,
high frequency data,
fractional Brownian motion,
adaptive estimation of quadratic functionals,
wavelet methods,
60G18,
62G99,
62F12,
62M09
@article{1194461718,
author = {Gloter, Arnaud and Hoffmann, Marc},
title = {Estimation of the Hurst parameter from discrete noisy data},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 1947-1974},
language = {en},
url = {http://dml.mathdoc.fr/item/1194461718}
}
Gloter, Arnaud; Hoffmann, Marc. Estimation of the Hurst parameter from discrete noisy data. Ann. Statist., Tome 35 (2007) no. 1, pp. 1947-1974. http://gdmltest.u-ga.fr/item/1194461718/