  We consider to model matrix time series based on a tensor CP-decomposition.
Instead of using an iterative algorithm which is the standard practice for
estimating CP-decompositions, we propose a new and one-pass estimation
procedure based on a generalized eigenanalysis constructed from the serial
dependence structure of the underlying process. To overcome the intricacy of
solving a rank-reduced generalized eigenequation, we propose a further refined
approach which projects it into a lower-dimensional full-ranked eigenequation.
This refined method improves significantly the finite-sample performance of the
estimation. The asymptotic theory has been established under a general setting
without the stationarity. It shows, for example, that all the component
coefficient vectors in the CP-decomposition are estimated consistently with
certain convergence rates. The proposed model and the estimation method are
also illustrated with both simulated and real data; showing effective
dimension-reduction in modelling and forecasting matrix time series.
