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Register a new userWavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes
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Added by
Francois Roueff
Publication date
2011
fields
Mathematical Statistics
and research's language is
English
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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 It^o 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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