Reduced-Rank Autoregressive Models for Matrix Time Series
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.
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BibTeX
@misc{xiao2026reducedrank,
title = {{Reduced-Rank Autoregressive Models for Matrix Time Series}},
author = {Han Xiao and Yuefeng Han and Rong Chen and Ama Ampadu-Kissi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28841},
eprint = {2609.28841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28841},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Reduced-Rank Autoregressive Models for Matrix Time Series
AU - Han Xiao
AU - Yuefeng Han
AU - Rong Chen
AU - Ama Ampadu-Kissi
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28841
UR - https://arxiv.org/abs/2609.28841
AB - 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.
ER -