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We consider stationary processes with long memory which are non-Gaussian andrepresented as Hermite polynomials of a Gaussian process. We focus on thecorresponding wavelet coefficients and study the asymptotic behavior of the sumof their squares since this sum is often used for estimating the long-memoryparameter. We show that the limit is not Gaussian but can be expressed usingthe non-Gaussian Rosenblatt process defined as a Wiener It\^o integral of order2. This happens even if the original process is defined through a Hermitepolynomial of order higher than 2.

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