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

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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. © 2010 Elsevier B.V. All rights reserved.

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Bardet, J. M., & Tudor, C. A. (2010). A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter. Stochastic Processes and Their Applications, 120(12), 2331–2362. https://doi.org/10.1016/j.spa.2010.08.003

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