Bayesian Dynamic Matrix Factor Models

The growth in data volume and the expansion in data dimensionality are challenging the analysis of high-dimensional matrix time series. Factor models for matrix-valued high-dimensional time series are a powerful tool for reducing the dimensionality of the variables with low-rank structures. However, existing high-dimensional matrix factor models are nearly all static and struggle to capture the dynamics and time evolution of data. In this article, a dynamic matrix factor model based on a numerically stable Bayesian algorithm is proposed to tackle the challenges mentioned above. In addition, the identification of dynamic matrix factor models is discussed and two methods for model identification are proposed. Additionally, a model comparison method for hyperparameter selection is proposed. The simulation results show that the proposed Bayesian dynamic matrix factor model can accurately estimate the matrix factors and obtain estimated confidence intervals. A real-world data analysis on a financial portfolio dataset illustrates that the method can be used to extract useful knowledge from high-dimensional matrix time series.