Generalized Spatial and Spatiotemporal Autoregressive Conditional Heteroscedasticity

TL;DR

This paper introduces a novel spatial ARCH model capturing heteroscedastic variance based on neighboring locations, extending the temporal ARCH to spatial and spatiotemporal contexts, with applications to modeling lung cancer mortality.

Contribution

It develops the first spatial ARCH model, demonstrates parameter estimation via maximum likelihood, and applies it to real-world health data, comparing it with benchmark models.

Findings

The spatial ARCH model effectively captures heteroscedasticity in spatial data.

Maximum likelihood estimation performs well in simulations.

The model provides better fit for lung cancer mortality data than benchmarks.

Abstract

In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We show additionally how the introduced spatial ARCH model can be used in spatiotemporal settings. In contrast to the temporal ARCH model, in which the distribution is known given the full information set of the prior periods, the distribution is not straightforward in the spatial and spatiotemporal setting. However, it is possible to estimate the parameters of the model using the maximum-likelihood approach. Via Monte Carlo simulations, we demonstrate the performance of the estimator for a specific spatial weighting matrix. Moreover, we combine the known spatial autoregressive model with the spatial ARCH model assuming heteroscedastic errors. Eventually, the proposed autoregressive process is illustrated using an empirical example. Specifically, we model lung cancer mortality in 3108 U.S. counties and compare the introduced model with two benchmark approaches.