Dynamic spatiotemporal ARCH models

Geo-referenced data are characterised by an inherent spatial dependence due to geographical proximity. In this paper, we introduce a dynamic spatiotemporal autoregressive conditional heteroscedasticity (ARCH) process to describe the effects of (i) the log-squared time-lagged outcome variable, the temporal effect, (ii) the spatial lag of the log-squared outcome variable, the spatial effect, and (iii) the spatiotemporal effect on the volatility of an outcome variable. We derive a generalised method of moments (GMM) estimator based on the linear and quadratic moment conditions. We show the consistency and asymptotic normality of the GMM estimator. After studying the finite-sample performance in simulations, the model is demonstrated by analysing monthly log-returns of condominium prices in Berlin from 1995 to 2015, for which we found significant volatility spillovers.