Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 42-76.

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.

DOI : 10.1051/ps/2012026
Classification : 42C40, 60G18, 62M15, 60G20, 60G22
Mots-clés : Hermite processes, wavelet coefficients, wiener chaos, self-similar processes, long-range dependence 
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     author = {Clausel, M. and Roueff, F. and Taqqu, M. S. and Tudor, C.},
     title = {Wavelet estimation of the long memory parameter for {Hermite} polynomial of gaussian processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {42--76},
     publisher = {EDP-Sciences},
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     mrnumber = {3143733},
     zbl = {1310.42023},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2012026/}
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Clausel, M.; Roueff, F.; Taqqu, M. S.; Tudor, C. Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 42-76. doi : 10.1051/ps/2012026. http://www.numdam.org/articles/10.1051/ps/2012026/

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