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We consider to model matrix time series based on a tensor CP-decomposition.Instead of using an iterative algorithm which is the standard practice forestimating CP-decompositions, we propose a new and one-pass estimationprocedure based on a generalized eigenanalysis constructed from the serialdependence structure of the underlying process. To overcome the intricacy ofsolving a rank-reduced generalized eigenequation, we propose a further refinedapproach which projects it into a lower-dimensional full-ranked eigenequation.This refined method improves significantly the finite-sample performance of theestimation. The asymptotic theory has been established under a general settingwithout the stationarity. It shows, for example, that all the componentcoefficient vectors in the CP-decomposition are estimated consistently withcertain convergence rates. The proposed model and the estimation method arealso illustrated with both simulated and real data; showing effectivedimension-reduction in modelling and forecasting matrix time series.

Modelling matrix time series via a tensor CP-decomposition