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
LJK - Laboratoire Jean Kuntzmann, ICJ - Institut Camille Jordan [Villeurbanne]
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
Type de document :
Article dans une revue
ESAIM: Probability and Statistics, EDP Sciences, 2014, 18, pp.42-76. 〈10.1051/ps/2012026〉
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Contributeur : François Roueff <>
Soumis le : vendredi 31 mai 2013 - 17:15:24
Dernière modification le : mercredi 12 décembre 2018 - 15:31:07
Document(s) archivé(s) le : dimanche 1 septembre 2013 - 07:50:08

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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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