English

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.

Keywords

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}
}
R2 v1 2026-06-21T16:28:27.156Z