Modelling matrix time series via a tensor CP-decomposition

Jinyuan Chang, Jing He, Lin Yang, Qiwei Yao

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2023 · Volume 85 · Issue 1

Abstract

We consider to model matrix time series based on a tensor canonical polyadic (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 can significantly improve the finite-sample performance. We show that all the component coefficient vectors in the CP-decomposition can be estimated consistently. 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.

Keywords

dimension-reduction, generalized eigenanalysis, matrix time series, tensor CP-decomposition

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