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

[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.

[发布日期] 2010-12-01

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