Asymptotic normality of wavelet covariances and multivariate wavelet Whittle estimators

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