  Multivariate processes with long-range dependence properties can be
encountered in many fields of application. Two fundamental characteristics in
such frameworks are long-range dependence parameters and correlations between
component time series. We consider multivariate long-range dependent linear
processes, not necessarily Gaussian. 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-range dependence
parameter and the long-run covariance by a wavelet-based Whittle procedure. We
prove the asymptotic normality of the estimators, and we provide an explicit
expression for the asymptotic covariances. An empirical illustration of this
result is proposed on a real dataset of rat brain connectivity.
