Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity

In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighbouring locations. The proposed process is considered as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We also show how the newly 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 for the prior periods, the distribution is not straightforward in the spatial and spatiotemporal setting. However, the model parameters can be estimated 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 by an empirical example. Specifically, we model lung cancer mortality in 3108 U.S. counties and compare the newly introduced model with four benchmark approaches.