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Autoregressive models for matrix-valued time series

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  • Chen, Rong
  • Xiao, Han
  • Yang, Dan

Abstract

In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each quarter neatly form a matrix and are observed over consecutive quarters. Dynamic transport networks with observations generated on the edges can be formed as a matrix observed over time. Although it is natural to turn the matrix observations into long vectors, then use the standard vector time series 2 models for analysis, it is often the case that the columns and rows of the matrix represent different types of structures that are closely interplayed. In this paper we follow the autoregression for modeling time series and propose a novel matrix autoregressive model in a bilinear form that maintains and utilizes the matrix structure to achieve a substantial dimensional reduction, as well as more interpretability. Probabilistic properties of the models are investigated. Estimation procedures with their theoretical properties are presented and demonstrated with simulated and real examples.

Suggested Citation

  • Chen, Rong & Xiao, Han & Yang, Dan, 2021. "Autoregressive models for matrix-valued time series," Journal of Econometrics, Elsevier, vol. 222(1), pages 539-560.
  • Handle: RePEc:eee:econom:v:222:y:2021:i:1:p:539-560
    DOI: 10.1016/j.jeconom.2020.07.015
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    Cited by:

    1. Matteo Barigozzi & Giuseppe Cavaliere & Graziano Moramarco, 2022. "Factor Network Autoregressions," Papers 2208.02925, arXiv.org, revised Feb 2024.
    2. Andrea Bucci, 2022. "A smooth transition autoregressive model for matrix-variate time series," Papers 2212.08615, arXiv.org.
    3. 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.
    4. Ruofan Yu & Rong Chen & Han Xiao & Yuefeng Han, 2024. "Dynamic Matrix Factor Models for High Dimensional Time Series," Papers 2407.05624, arXiv.org.
    5. Benth, Fred Espen & Karbach, Sven, 2023. "Multivariate continuous-time autoregressive moving-average processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 299-337.
    6. Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).
    7. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    8. Wei Zhang, 2024. "Bayesian Dynamic Factor Models for High-dimensional Matrix-valued Time Series," Papers 2409.08354, arXiv.org.
    9. He, Yong & Kong, Xinbing & Trapani, Lorenzo & Yu, Long, 2023. "One-way or two-way factor model for matrix sequences?," Journal of Econometrics, Elsevier, vol. 235(2), pages 1981-2004.
    10. Cheng Yu & Dong Li & Feiyu Jiang & Ke Zhu, 2023. "Matrix GARCH Model: Inference and Application," Papers 2306.05169, arXiv.org.
    11. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.

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