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

J.-M. Bardet and C.A. Tudor

Stochastic Processes and their Applications, 2010, vol. 120, issue 12, 2331-2362

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: Multiple; Wiener-Ito; integral; Wavelet; analysis; Rosenblatt; process; Fractional; Brownian; motion; Noncentral; limit; theorem; Self-similarity; Parameter; estimation (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (11)

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