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arXiv · 1010.2895

Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Jean-Marc Bardet·Donatas Surgailis
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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.

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BibTeXRIS

Jean-Marc Bardet, Donatas Surgailis. 2012-06-07. Nonparametric estimation of the local Hurst function of multifractional Gaussian processes. https://doi.org/10.1016/j.spa.2012.11.009

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