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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Bardet, J-M¹  Tudor, C. A.² 

[1] Univ Paris 01, SAMM, F-75534 Paris, France

[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

关键词: Multiple Wiener-Ito integral;    Wavelet analysis;    Rosenblatt process;    Fractional Brownian motion;    Noncentral limit theorem;    Self-similarity;    Parameter estimation;   

DOI  :  10.1016/j.spa.2010.08.003

来源: Elsevier

【 摘 要 】

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 coefficient; 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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free