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Modelling matrix time series via a tensor CP-decomposition

Author

Listed:
  • Chang, Jinyuan
  • Zhang, Henry
  • Yang, Lin
  • Yao, Qiwei

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.

Suggested Citation

  • Chang, Jinyuan & Zhang, Henry & Yang, Lin & Yao, Qiwei, 2023. "Modelling matrix time series via a tensor CP-decomposition," LSE Research Online Documents on Economics 117644, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:117644
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    File URL: http://eprints.lse.ac.uk/117644/
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    References listed on IDEAS

    as
    1. Yuefeng Han & Dan Yang & Cun-Hui Zhang & Rong Chen, 2021. "CP Factor Model for Dynamic Tensors," Papers 2110.15517, arXiv.org, revised Apr 2024.
    2. Elynn Y. Chen & Ruey S. Tsay & Rong Chen, 2020. "Constrained Factor Models for High-Dimensional Matrix-Variate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 775-793, April.
    3. Chen, Rong & Xiao, Han & Yang, Dan, 2021. "Autoregressive models for matrix-valued time series," Journal of Econometrics, Elsevier, vol. 222(1), pages 539-560.
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    6. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2015. "High dimensional stochastic regression with latent factors, endogeneity and nonlinearity," LSE Research Online Documents on Economics 61886, London School of Economics and Political Science, LSE Library.
    7. Elynn Y. Chen & Rong Chen, 2019. "Modeling Dynamic Transport Network with Matrix Factor Models: with an Application to International Trade Flow," Papers 1901.00769, arXiv.org.
    8. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    9. Wang, Dong & Liu, Xialu & Chen, Rong, 2019. "Factor models for matrix-valued high-dimensional time series," Journal of Econometrics, Elsevier, vol. 208(1), pages 231-248.
    10. Chang, Jinyuan & Guo, Bin & Yao, Qiwei, 2018. "Principal component analysis for second-order stationary vector time series," LSE Research Online Documents on Economics 84106, London School of Economics and Political Science, LSE Library.
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    More about this item

    Keywords

    dimension-reduction; generalized eigenanalysis; tensor CP-decomposition; matrix time series;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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