HAL : hal-00526294, version 2

arXiv : 1010.2895

DOI : 10.1016/j.spa.2012.11.009

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Stochastic Processes and their Applications 123, 3 (2013) 1004-1045

Versions disponibles :

v1 (14-10-2010)

v2 (07-06-2012)

Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Jean-Marc Bardet 1, Donatas Surgailis 2, 3

(2013)

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.

1 :	Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)
	Université Paris I - Panthéon-Sorbonne
2 :	Vilnius Institute of Mathematics and Informatics
	Vilnius University
3 :	Institute of Mathematics and Informatics
	Université de Vilnius

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Nonparametric estimators – Hurst function – tangent process – multifractional Brownian motion – Gaussian process – limit theorems.

hal-00526294, version 2

http://hal.archives-ouvertes.fr/hal-00526294

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Contributeur : Jean-Marc Bardet <>

Soumis le : Jeudi 7 Juin 2012, 11:03:37

Dernière modification le : Jeudi 28 Février 2013, 21:34:25