In this paper, a general overview on spatial and spatiotemporal ARCH models
is provided. In particular, we distinguish between three different spatial
ARCH-type models. In addition to the original definition of Otto et al. (2016),
we introduce an exponential spatial ARCH model in this paper. For this new
model, maximum-likelihood estimators for the parameters are proposed. In
addition, we consider a new complex-valued definition of the spatial ARCH
process. From a practical point of view, the use of the R-package spGARCH is
demonstrated. To be precise, we show how the proposed spatial ARCH models can
be simulated and summarize the variety of spatial models, which can be
estimated by the estimation functions provided in the package. Eventually, we
apply all procedures to a real-data example