  Time series of matrix-valued data are increasingly available in various areas
including economics, finance, social science, etc. These data may shed light on
the inter-dynamical relationships between two sets of attributes, for instance
countries and economic indices. The matrix autoregressive (MAR) model provides
a parsimonious approach for analyzing such data. However, the MAR model, being
a linear model with parametric constraints, cannot capture the nonlinear
patterns in the data, such as regime shifts in the dynamics. We propose a
mixture matrix autoregressive (MMAR) model for analyzing potential regime
shifts in the dynamics between two attributes, for instance, due to recession
vs. blooming, or quiet period vs. pandemic. We propose an EM algorithm for
maximum likelihood estimation. We derive some theoretical properties of the
proposed method including consistency and asymptotic distribution, and
illustrate its performance via simulations and real applications.
