Asymptotic normality of wavelet covariances and of multivariate wavelet Whittle estimators
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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.
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