  The space time autoregressive model has been widely applied in science, in
areas such as economics, public finance, political science, agricultural
economics, environmental studies and transportation analyses. The classical
space time autoregressive model is a linear model for describing spatial
correlation. In this work, we expand the classical model to include related
exogenous variables, possibly non-Gaussian, high volatility errors, and a
nonlinear neural network component. The nonlinear neural network component
allows for more model flexibility, the ability to learn and model nonlinear and
complex relationships. We use a maximum likelihood approach for model parameter
estimation. We establish consistency and asymptotic normality for these
estimators under some standard conditions on the space time model and neural
network component. We investigate the quality of the asymptotic approximations
for finite samples by means of numerical simulation studies. For illustration,
we include a real world application.
