# Partially Specified Space Time Autoregressive Model with Artificial Neural Network

## TL;DR

This paper extends the classical space-time autoregressive model by integrating exogenous variables, non-Gaussian errors, and a neural network component, enhancing flexibility and modeling complex spatial-temporal relationships.

## Contribution

It introduces a partially specified space-time autoregressive model with neural networks, providing estimation methods and theoretical properties like consistency and asymptotic normality.

## Key findings

- Neural network component improves model flexibility.
- Simulation studies validate finite sample approximations.
- Real-world application demonstrates practical utility.

## Abstract

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.