Dynamic Spatiotemporal ARCH Models: Small and Large Sample Results

This paper explores the estimation of a dynamic spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model. The log-volatility term in this model can depend on (i) the spatial lag of the log-squared outcome variable, (ii) the time-lag of the log-squared outcome variable, (iii) the spatiotemporal lag of the log-squared outcome variable, (iv) exogenous variables, and (v) the unobserved heterogeneity across regions and time, i.e., the regional and time fixed effects. We examine the small and large sample properties of two quasi-maximum likelihood estimators and a generalized method of moments estimator for this model. We first summarize the theoretical properties of these estimators and then compare their finite sample properties through Monte Carlo simulations.