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

## TL;DR

This paper introduces the spGARCH R-package for modeling spatial and spatiotemporal ARCH processes, including new models and estimation methods, demonstrated through simulations and a real-data application.

## Contribution

It presents new spatial ARCH models, including an exponential variant and a complex-valued form, with maximum-likelihood estimators and practical implementation in R.

## Key findings

- Successful simulation of spatial ARCH models
- Estimation of models using the spGARCH package
- Application to real spatial data example

## Abstract

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.