Generalized Spatial and Spatiotemporal ARCH Models

TL;DR

This paper introduces a novel spatial GARCH model that captures spatial dependence and spill-overs in volatility, unifying existing models and demonstrating its application to real estate data in Berlin.

Contribution

It proposes a unified spatial and spatiotemporal GARCH framework that includes all previous models and allows for instantaneous spill-overs across spatial units.

Findings

Model successfully captures local risk clusters.

Monte Carlo simulations validate estimation approach.

Empirical analysis of Berlin real estate prices demonstrates model utility.

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 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.