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

M. Clausel; F. Roueff; M. S. Taqqu; C. Tudor

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 42-76
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Clausel, M., et al. "Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes." ESAIM: Probability and Statistics 18 (2014): 42-76. <http://eudml.org/doc/273645>.

@article{Clausel2014,
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.},
author = {Clausel, M., Roueff, F., Taqqu, M. S., Tudor, C.},
journal = {ESAIM: Probability and Statistics},
keywords = {Hermite processes; wavelet coefficients; wiener chaos; self-similar processes; long–range dependence; wavelet analysis; non-Gaussian stochastic processes; scalogram; long memory parameter; Wiener chaos; Hermite polynomial; Rosenblatt process},
language = {eng},
pages = {42-76},
publisher = {EDP-Sciences},
title = {Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes},
url = {http://eudml.org/doc/273645},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Clausel, M.
AU - Roueff, F.
AU - Taqqu, M. S.
AU - Tudor, C.
TI - Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 42
EP - 76
AB - 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.
LA - eng
KW - Hermite processes; wavelet coefficients; wiener chaos; self-similar processes; long–range dependence; wavelet analysis; non-Gaussian stochastic processes; scalogram; long memory parameter; Wiener chaos; Hermite polynomial; Rosenblatt process
UR - http://eudml.org/doc/273645
ER -

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