A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter

J. M. Bardet; C. A. Tudor

doi:10.1016/j.spa.2010.08.003

A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter

J. M. Bardet
, C. A. Tudor

Université Panthéon-Sorbonne (Paris 1)
CNRS UMR 8524

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

43 Citations (Scopus)

Résumé

By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations.

langue originale	Anglais
Pages (de - à)	2331-2362
Nombre de pages	32
journal	Stochastic Processes and their Applications
Volume	120
Numéro de publication	12
Les DOIs	https://doi.org/10.1016/j.spa.2010.08.003
état	Publié - 1 déc. 2010
Modification externe	Oui

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title = "A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter",

abstract = "By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations.",

keywords = "Fractional Brownian motion, Multiple Wiener-It integral, Noncentral limit theorem, Parameter estimation, Rosenblatt process, Self-similarity, Wavelet analysis",

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TY - JOUR

T1 - A wavelet analysis of the Rosenblatt process

T2 - Chaos expansion and estimation of the self-similarity parameter

AU - Bardet, J. M.

AU - Tudor, C. A.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations.

AB - By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations.

KW - Fractional Brownian motion

KW - Multiple Wiener-It integral

KW - Noncentral limit theorem

KW - Parameter estimation

KW - Rosenblatt process

KW - Self-similarity

KW - Wavelet analysis

U2 - 10.1016/j.spa.2010.08.003

DO - 10.1016/j.spa.2010.08.003

M3 - Article

AN - SCOPUS:77957754964

SN - 0304-4149

VL - 120

SP - 2331

EP - 2362

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 12

ER -

A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter

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