  We consider linear processes, not necessarily Gaussian, with long, short or
negative memory. The memory parameter is estimated semi-parametrically using
wavelets from a sample $X_1,...,X_n$ of the process. We treat both the
log-regression wavelet estimator and the wavelet Whittle estimator. We show
that these estimators are asymptotically normal as the sample size $n\to\infty$
and we obtain an explicit expression for the limit variance. These results are
derived from a general result on the asymptotic normality of the empirical
scalogram for linear processes, conveniently centered and normalized. The
scalogram is an array of quadratic forms of the observed sample, computed from
the wavelet coefficients of this sample. In contrast with quadratic forms
computed on the Fourier coefficients such as the periodogram, the scalogram
involves correlations which do not vanish as the sample size $n\to\infty$.
