Matrix-Valued Spatial Autoregressions with Dynamic and Robust Heterogeneous Spillovers

We introduce a new time-varying parameter spatial matrix autoregressive model that integrates matrix-valued time series, heterogeneous spillover effects, outlier robustness, and time-varying parameters in one unified framework. The model allows for separate dynamic spatial spillover effects across both the row and column dimensions of the matrix-valued observations. Robustness is introduced through innovations that follow a (conditionally heteroskedastic) matrix Student's $t$ distribution. In addition, the proposed model nests many existing spatial autoregressive models, yet remains easy to estimate using standard maximum likelihood methods. We establish the stationarity and invertibility of the model and the consistency and asymptotic normality of the maximum likelihood estimator. Our simulations reveal that the latent time-varying two-way spatial spillover effects can be successfully recovered, even under severe model misspecification. The model's usefulness is illustrated both in-sample and out-of-sample using two different applications: one in international trade, and the other based on global stock market data.