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

2011/05/05 by Marianne Clausel, Clausel, Marianne, François Roueff +5 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Image and Signal Denoising Methods #Statistical and numerical algorithms #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1105.1011

openalex publication_date 2011/05/05 · arxiv created 2013/06/01 · arxiv updated 2013/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• High order chaotic limits of wavelet scalograms under long--range dependence

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