A note on dynamic spatiotemporal ARCH models: small- and large-sample results

This short 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 generalised 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.