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Reduced-Rank Autoregressive Models for Matrix Time Series

Han Xiao, Yuefeng Han, Rong Chen, Ama Ampadu-Kissi

arXiv 23 Sep 2026 · Statistics — Methodology

arXiv:2609.28841 · PDF · Extracted main text

Abstract

Matrix time series is a series of matrix data observed over time. Analytical tools for such time series is needed in many applications in finance, economics, engineering and many other fields. To avoid the use of vectorization of the matrices which loses the column and row information, and the vector autoregression framework in traditional time series analysis, \cite{chen2021autoregressive} proposed the Matrix Autoregressive (MAR) Model. The model maintains and utilizes the matrix structure, leading to a substantial dimensional reduction and admitting explicit interpretations, comparing with the vector autoregressive model on the vectorized data. However, the MAR model still encounters difficulties in dealing with large dimensional matrix time series as the coefficient matrices in MAR models are also large. In this paper we propose to achieve further dimension reduction through reduced-rank constraints of the coefficient matrices in the MAR model. Estimation and rank determination procedures are studied. Theoretical investigation and empirical examples show that the reduced-rank constraint can achieve higher statistical efficiency than the MAR model.

Citation extraction

72
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in-text mentions
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
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3Anderson, T. W (2003) An introduction to multivariate statistical analysis0.92843100%
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5Chen, Rong and Yang, Dan and Zhang, Cun-Hui (2021) Factor models for high-dimensional tensor time series self0.73732100%
6Anderson, T. W (1951) Estimating linear restrictions on regression coefficients for multivariate normal distributions0.64422100%
7Basu, Sumanta and Li, Xianqi and Michailidis, George (2019) Low rank and structured modeling of high-dimensional vector autoregressions0.64422100%
8Lin, Jiahe and Michailidis, George (2020) Regularized Estimation of High-dimensional Factor-Augmented Vector Autoregressive (FAVAR) Models0.64422100%
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10Hoff, Peter D (2011) Separable covariance arrays via the Tucker product, with applications to multivariate relational data0.51121100%

Showing the top 10 of 72 scored citations.