A Hybrid Framework Combining Autoregression and Common Factors for Matrix Time Series Modeling

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.