Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Bardet, Jean-Marc¹  Surgailis, Donatas² 

[1] Univ Paris 01, SAMM, F-75634 Paris, France

[2] Inst Math & Informat, Vilnius, Lithuania

关键词: Nonparametric estimators;    Hurst function;    Tangent process;    Multifractional Brownian motion;    Gaussian process;    Central limit theorem;   

DOI  :  10.1016/j.spa.2012.11.009

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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