  In time-series analyses, particularly for finance, generalized autoregressive
conditional heteroscedasticity (GARCH) models are widely applied statistical
tools for modelling volatility clusters (i.e., periods of increased or
decreased risk). In contrast, it has not been considered to be of critical
importance until now to model spatial dependence in the conditional second
moments. Only a few models have been proposed for modelling local clusters of
increased risks. In this paper, we introduce novel spatial GARCH and
exponential GARCH processes in a unified spatial and spatiotemporal GARCH-type
model, which also covers all previously proposed spatial ARCH models as well as
time-series GARCH models. For this common modelling framework, estimators are
derived based on nonlinear least squares and on the maximum-likelihood
approach. In addition to the theoretical contributions of this paper, we
suggest a model selection strategy that is verified by a series of Monte Carlo
simulation studies. Eventually, the use of the unified model is demonstrated by
an empirical example that focuses on real estate prices from 1995 to 2014
across the ZIP-Code areas of Berlin. A spatial autoregressive model is applied
to the data to illustrate how locally varying model uncertainties can be
captured by the spatial GARCH-type models.
