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Journal Articles ESAIM: Probability and Statistics Year : 2014

Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes

Abstract

We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long-memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener Itô integral of order 2. This happens even if the original process is defined through a Hermite polynomial of order higher than 2.
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Dates and versions

hal-00590798 , version 1 (05-05-2011)
hal-00590798 , version 2 (01-07-2011)
hal-00590798 , version 3 (31-05-2013)

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Marianne Clausel, François Roueff, Murad S. Taqqu, Ciprian A. Tudor. Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes. ESAIM: Probability and Statistics, 2014, 18, pp.42-76. ⟨10.1051/ps/2012026⟩. ⟨hal-00590798v3⟩
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