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.