Nonparametric estimation of the local Hurst function of multifractional Gaussian processes
Statistics Theory
2012-11-29 v2 Statistics Theory
Abstract
A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.
Cite
@article{arxiv.1010.2895,
title = {Nonparametric estimation of the local Hurst function of multifractional Gaussian processes},
author = {Jean-Marc Bardet and Donatas Surgailis},
journal= {arXiv preprint arXiv:1010.2895},
year = {2012}
}