  Multivariate processes with long-range memory properties can be encountered
in many applications fields. Two fundamentals characteristics in such
frameworks are the long-memory parameters and the correlation between time
series. We consider multivariate linear processes, not necessarily Gaussian,
presenting long-memory dependence. We show that the covariances between the
wavelet coefficients in this setting are asymptotically Gaussian. We also study
the asymptotic distributions of the estimators of the long-memory parameter and
of the long-run covariance by a wavelet-based Whittle procedure. We prove the
asymptotic normality of the estimators and we give an explicit expression for
the asymptotic covariances. An empirical illustration of this result is
proposed on a real dataset of a rat brain connectivity.
