  Matrix time series, which consist of matrix-valued data observed over time,
are prevalent in various fields such as economics, finance, and engineering.
Such matrix time series data are often observed in high dimensions. Matrix
factor models are employed to reduce the dimensionality of such data, but they
lack the capability to make predictions without specified dynamics in the
latent factor process. To address this issue, we propose a two-component
dynamic matrix factor model that extends the standard matrix factor model by
incorporating a matrix autoregressive structure for the low-dimensional latent
factor process. This two-component model injects prediction capability to the
matrix factor model and provides deeper insights into the dynamics of
high-dimensional matrix time series. We present the estimation procedures of
the model and their theoretical properties, as well as empirical analysis of
the estimation procedures via simulations, and a case study of New York city
taxi data, demonstrating the performance and usefulness of the model.
