Zhiyun Fan, Xiaoyu Zhang, Mingyang Chen, Di Wang
arXiv 7 Mar 2025 · Statistics — Methodology
arXiv:2503.05340 · PDF · DOI · OpenAlex · Extracted main text
Matrix-valued time series are increasingly common in economics and finance, but existing approaches such as matrix autoregressive and dynamic matrix factor models often impose restrictive assumptions and fail to capture complex dependencies. We propose a hybrid framework that integrates autoregressive dynamics with a shared low-rank common factor structure, enabling flexible modeling of temporal dependence and cross-sectional correlation while achieving dimension reduction. The model captures dynamic relationships through lagged matrix terms and leverages low-rank structures across predictor and response matrices, with connections between their row and column subspaces established via common latent bases to improve interpretability and efficiency. We develop a computationally efficient gradient-based estimation method and establish theoretical guarantees for statistical consistency and algorithmic convergence. Extensive simulations show robust performance under various data-generating processes, and in an application to multinational macroeconomic data, the model outperforms existing methods in forecasting and reveals meaningful interactions among economic factors and countries. The proposed framework provides a practical, interpretable, and theoretically grounded tool for analyzing high-dimensional matrix time series.
appendix boundary found by appendix_command · 30% of the source is main text. Read the extracted text to check this.
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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen, R., Xiao, H., and Yang, D (2021) Autoregressive models for matrix-valued time series | 1.000 | 5 | 3 | 100% |
| 2 | Xiao, H., Han, Y., Chen, R., and Liu, C (2023) Reduced-rank autoregressive models for matrix time series | 0.874 | 6 | 4 | 67% |
| 3 | Huang, F., Lu, K., Zheng, Y., and Li, G (2025) Supervised factor modeling for high-dimensional linear time series | 0.737 | 3 | 2 | 100% |
| 4 | Wang, D., Liu, X., and Chen, R (2019) Factor models for matrix-valued high-dimensional time series self | 0.737 | 3 | 2 | 100% |
| 5 | Wang, D., Zhang, X., Li, G., and Tsay, R (2023) High-dimensional vector autoregression with common response and predictor factors self | 0.693 | 9 | 5 | 33% |
| 6 | Chen, E. Y., Tsay, R. S., and Chen, R (2020) Constrained factor models for high-dimensional matrix-variate time series | 0.644 | 2 | 2 | 100% |
| 7 | Lam, C. and Yao, Q (2012) Factor modeling for high-dimensional time series: Inference for the number of factors | 0.644 | 2 | 2 | 100% |
| 8 | Tu, S., Boczar, R., Simchowitz, M., Soltanolkotabi, M., and Recht, B (2016) Low-rank solutions of linear matrix equations via procrustes flow | 0.511 | 3 | 2 | 33% |
| 9 | Basu, S. and Michailidis, G (2015) Regularized estimation in sparse high-dimensional time series models | 0.511 | 2 | 2 | 50% |
| 10 | Wang, L., Zhang, X., and Gu, Q (2017) A Unified Computational and Statistical Framework for Nonconvex Low-rank Matrix Estimation self | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 40 scored citations.