Title :

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

Author(s) :

Clausel, Marianne [Auteur]
Statistique Apprentissage Machine [SAM]
Roueff, François [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Taqqu, Murad [Auteur]
Boston University [Boston] [BU]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

ESAIM: Probability and Statistics

Pages :

42-76

Publisher :

EDP Sciences

Publication date :

2014-01

ISSN :

1292-8100

English keyword(s) :

Hermite processes
Wavelet coefficients
Wiener chaos
self-similar processes
Long--range dependence

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL