A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter |
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Authors: | J-M Bardet CA Tudor |
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Institution: | 1. SAMM, Université de Paris 1, 90, rue de Tolbiac, 75634, Paris, France;2. Laboratoire Paul Painlevé, Université de Lille 1, F-59655 Villeneuve d’Ascq, France |
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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. |
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Keywords: | primary 60G18 secondary 60F05 60H05 62F12 |
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