  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.
