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arXiv · 1105.1011

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

Marianne Clausel·François Roueff·Murad S. Taqqu·Ciprian A. Tudor
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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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Marianne Clausel, François Roueff, Murad S. Taqqu, Ciprian A. Tudor. 2013-06-01. Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes. https://arxiv.org/abs/1105.1011

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