Spatial and Spatiotemporal GARCH Models -- A Unified Approach

TL;DR

This paper introduces a unified spatial and spatiotemporal GARCH modeling framework that captures local risk clusters in spatial data, extending traditional time-series GARCH models to spatial contexts with theoretical and empirical validation.

Contribution

It proposes novel spatial GARCH and exponential GARCH processes within a unified framework, covering existing models and providing estimation methods and model selection strategies.

Findings

Successfully models local risk clusters in spatial data.

Demonstrates improved risk modeling in real estate prices.

Validates the approach with Monte Carlo simulations.

Abstract

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.