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.

翻译：本文探讨了动态时空自回归条件异方差（ARCH）模型的估计问题。该模型中的对数波动项可能依赖于：（i）对数平方结果变量的空间滞后项，（ii）对数平方结果变量的时间滞后项，（iii）对数平方结果的时空滞后项，（iv）外生变量，以及（v）区域和时间的未观测异质性，即区域固定效应和时间固定效应。我们研究了该模型的两种拟极大似然估计量和一种广义矩估计量在小样本和大样本下的性质。首先总结了这些估计量的理论性质，然后通过蒙特卡洛模拟比较了它们的有限样本性质。