Geo-referenced data are characterised by an inherent spatial dependence due to the 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, i.e., the temporal effect, (ii) the spatial lag of the log-squared outcome variable, i.e., the spatial effect, and (iii)  the spatial lag of the log-squared time-lagged outcome variable, i.e., the spatiotemporal effect, on the volatility of an outcome variable. Furthermore, our suggested process allows for the fixed effects over time and space to account for the unobserved heterogeneity. For this dynamic spatiotemporal ARCH model, we derive a generalised method of moments (GMM) estimator based on the linear and quadratic moment conditions of a specific transformation. We show the consistency and asymptotic normality of the GMM estimator, and determine the best set of moment functions. We investigate the finite-sample properties of the proposed GMM estimator in a series of Monte-Carlo simulations with different model specifications and error distributions. Our simulation results show that our suggested GMM estimator has good finite sample properties. In an empirical application, we use monthly log-returns of the average condominium prices of each postcode of Berlin from 1995 to 2015 (190 spatial units, 240 time points) to demonstrate the use of our suggested model. Our estimation results show that  the temporal, spatial and spatiotemporal lags of the log-squared returns have statistically significant effects on the volatility of the log-returns.

Speaker | Prof. Philipp Otto 
Geo-Passionate data scientist and professor of “Big Geospatial Data” with an interdisciplinary research profile and several publications in outstanding scientific journals (rated as top 9% scientist with their first publication in 2016 on ResearchGate). Supervised 20+ B.Sc. and M.Sc. theses, 7 Ph.D. dissertations (6 ongoing, 1 complete) with strong philosophy of teaching environmetrics. In his young academic career since 2016, when he did his Ph.D. in statistics, he received research grants of over 1,000,000 Euros. He is also actively involved in the scientific community as associate editor of 3 journals and treasurer of the German Statistical Society.