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

Marianne Clausel 1 François Roueff 2 Murad Taqqu 3 Ciprian Tudor 4
1 SAM - Statistique Apprentissage Machine
LJK - Laboratoire Jean Kuntzmann
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 BU - Boston University [Boston]
4 LPP - Laboratoire Paul Painlevé - UMR 8524
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.
Keywords : Hermite processes Wavelet coefficients Wiener chaos self-similar processes Long--range dependence
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Journal articles
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Contributor : François Roueff <>
Submitted on : Friday, May 31, 2013 - 5:15:24 PM
Last modification on : Thursday, October 17, 2019 - 12:36:09 PM
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Marianne Clausel, François Roueff, Murad Taqqu, Ciprian Tudor. Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes. ESAIM: Probability and Statistics, EDP Sciences, 2014, 18, pp.42-76. ⟨10.1051/ps/2012026⟩. ⟨hal-00590798v3⟩

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