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

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.F. Roueff's research was partially supported by the ANR project MATAIM NT09 441552. Murad S. Taqqu was supported in part by the NSF grants DMS-0608669 and DMS-1007616 at Boston University. (NT09 441552 - ANR project MATAIM; DMS-0608669 - NSF at Boston University; DMS-1007616 - NSF at Boston University)Accepted manuscrip