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Multivariate Wavelet Whittle Estimation in Long‐range Dependence

Multivariate processes with long‐range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real‐data applications, the correlation between time series is crucial. Usual estimations of correlation can be highly biased owing to phase shifts caused by the differences in the properties of autocorrelation in the processes. To address this issue, we introduce a semiparametric estimation of multivariate long‐range dependent processes. The parameters of interest in the model are the vector of the long‐range dependence parameters and the long‐run covariance matrix, also called functional connectivity in neuroscience. This matrix characterizes coupling between time series. The proposed multivariate wavelet‐based Whittle estimation is shown to be consistent for the estimation of both the long‐range dependence and the covariance matrix and to encompass both stationary and nonstationary processes. A simulation study and a real‐data example are presented to illustrate the finite‐sample behaviour.