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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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Preprints, Working Papers, ...
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https://hal-imt.archives-ouvertes.fr/hal-00590798
Contributor : François Roueff <>
Submitted on : Thursday, May 5, 2011 - 10:07:39 AM
Last modification on : Friday, July 31, 2020 - 10:44:07 AM
Long-term archiving on: : Saturday, August 6, 2011 - 2:41:40 AM

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  • HAL Id : hal-00590798, version 1
  • ARXIV : 1105.1011

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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. 2011. ⟨hal-00590798v1⟩

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