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arXiv · 2112.15423

Modelling matrix time series via a tensor CP-decomposition

Jinyuan Chang·Jing He·Lin Yang·Qiwei Yao
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Abstract

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.

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Jinyuan Chang, Jing He, Lin Yang, Qiwei Yao. 2021-12-31. Modelling matrix time series via a tensor CP-decomposition. https://doi.org/10.1093/jrsssb%2Fqkac011

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