Modelling matrix time series via a tensor CP-decomposition
This work addresses dimension reduction in matrix time series forecasting, offering a novel estimation method that is incremental in improving computational efficiency and accuracy for time series analysis.
The authors tackled the problem of modeling matrix time series by proposing a tensor CP-decomposition model with a one-pass estimation procedure based on generalized eigenanalysis, which improves finite-sample performance and achieves consistent estimation of component vectors with specific convergence rates, as demonstrated in simulations and real data.
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.