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In this paper, a general overview on spatial and spatiotemporal ARCH modelsis provided. In particular, we distinguish between three different spatialARCH-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 newmodel, maximum-likelihood estimators for the parameters are proposed. Inaddition, we consider a new complex-valued definition of the spatial ARCHprocess. From a practical point of view, the use of the R-package spGARCH isdemonstrated. To be precise, we show how the proposed spatial ARCH models canbe simulated and summarize the variety of spatial models, which can beestimated by the estimation functions provided in the package. Eventually, weapply all procedures to a real-data example.

spGARCH: An R-Package for Spatial and Spatiotemporal ARCH models