  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 a novel spatial GARCH process in a
unified spatial and spatiotemporal GARCH framework, which also covers all
previously proposed spatial ARCH models, exponential spatial GARCH, and
time-series GARCH models. In contrast to previous spatiotemporal and time
series models, this spatial GARCH allows for instantaneous spill-overs across
all spatial units. For this common modelling framework, estimators are derived
based on a non-linear least-squares approach. Eventually, the use of the model
is demonstrated by a Monte Carlo simulation study and 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 (e.g., due to latent regressors) can be
captured by the spatial GARCH-type models.

Methodology;Econometrics