  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.
