Abstract

Matrix-variate time series data are increasingly popular in economics, statistics, and environmental

studies, among other fields. The bilinear autoregressive structure is a popular modeling approach for such data,

as it reduces model complexity while capturing dynamic interactions between rows and columns. However, in

high-dimensional settings, the conventional iterated least-squares method requires estimating a large number of

parameters, which hampers interpretability and scalability. To address this challenge, we propose regularized

estimation procedures designed for settings in which the autoregressive coefficient matrices exhibit banded

or sparse structures. Specifically, we introduce a Bayesian Information Criterion (BIC)-based approach to

estimate the bandwidth in the banded case, and employ the LASSO technique for enforcing sparsity in the

coefficient matrices. We derive asymptotic properties for both methods as the dimensions diverge and the

sample size T →∞. Simulations and real data examples demonstrate the effectiveness of our methods,

comparing their forecasting performance against common autoregressive models in the literature.

Information

Preprint No.SS-2024-0341
Manuscript IDSS-2024-0341
Complete AuthorsHangjin Jiang, Baining Shen, Yuzhou Li, Zhaoxing Gao
Corresponding AuthorsZhaoxing Gao
Emailsmazxgao@gmail.com

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Acknowledgments

We thank the Editor, Associate Editor, and anonymous referees for their constructive comments and valuable suggestions, which have greatly improved the presentation and quality of

this article. Z.G. acknowledges partial support from the National Natural Science Foundation

of China (NSFC) under Grant Nos. 12201558, 72573029, and U23A2064, and from the Tianfu

Emei Youth Talent Project of Sichuan Province. H.J. acknowledges partial support from the

High-level Talent Special Support Program of Zhejiang Province and the National Natural

Regularized Estimation of MAR Models

Science Foundation of China (No.12531013).

Supplementary Materials

The online Supplementary Material provides additional simulation results and proofs of the

theoretical results.

Supplementary materials are available for download.