Lin, Y., Lucas, A. and Ye, S. (2026). Matrix-valued spatial autoregressions with dynamic heterogeneous spillovers Journal of Econometrics, 258:106323.

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 can be introduced via a matrix Student{\textquoteright}s t distribution. The model can still be estimated straightforwardly by standard maximum likelihood methods, and we establish stationarity and invertibility of the model, as well as consistency and asymptotic normality of its maximum likelihood estimator. Simulations reveal that the two-way spatial spillover dynamics can be successfully recovered even if the model is misspecified. Using a 12  ×  12 trade network application, we show that the time-varying, robust matrix features of the new model better fit the empirical data than alternative specifications.