Modelling matrix time series via a tensor CP-decomposition

Jinyuan Chang, Henry Zhang, Lin Yang and Qiwei Yao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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; tensor CP-decomposition; matrix time series (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2023-02-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (1)

Published in Journal of the Royal Statistical Society. Series B: Statistical Methodology, 1, February, 2023, 85(1), pp. 127 – 148. ISSN: 1369-7412

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:117644

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