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.

翻译：矩阵值时间序列在经济学与金融学中日益普遍，但现有方法如矩阵自回归模型和动态矩阵因子模型通常施加了限制性假设，且难以捕捉复杂的依赖关系。本文提出一种混合框架，将自回归动态与共享的低秩公共因子结构相结合，从而在实现降维的同时，能够灵活地建模时间依赖性与横截面相关性。该模型通过滞后矩阵项捕捉动态关系，并利用预测矩阵与响应矩阵间的低秩结构，通过公共潜在基建立其行空间与列空间之间的关联，以提高可解释性与效率。我们开发了一种计算高效的基于梯度的估计方法，并建立了统计一致性与算法收敛性的理论保证。大量模拟实验表明，该模型在各种数据生成过程中均表现出稳健的性能；在一项跨国宏观经济数据的应用中，该模型在预测方面优于现有方法，并揭示了经济因子与国家间有意义的交互作用。所提出的框架为分析高维矩阵时间序列提供了一种实用、可解释且理论依据充分的工具。