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

Abstract: Matrix-valued time series analysis has gained prominence in econometrics and finance due to the increasing availability of high-dimensional data with inherent matrix structures. Traditional approaches, such as Matrix Autoregressive (MAR) models and Dynamic Matrix Factor (DMF) models, often impose restrictive assumptions that may not align with real-world data complexities. To address this gap, we propose a novel Matrix Autoregressive with Common Factors (MARCF) model, which bridges the gap between MAR and DMF frameworks by introducing common bases between predictor and response subspaces. The MARCF model achieves significant dimension reduction and enables a more flexible and interpretable factor representation of dynamic relationships. We develop a computationally efficient estimator and a gradient descent algorithm. Theoretical guarantees for computational and statistical convergence are provided, and extensive simulations demonstrate the robustness and accuracy of the model. Applied to a multinational macroeconomic dataset, the MARCF model outperforms existing methods in forecasting and provides meaningful insights into the interplay between countries and economic factors.