Bayesian inference in spatial GARCH models: an application to US house price returns

In this paper we consider a high-order spatial generalized autoregressive conditional heteroskedasticity (GARCH) model to account for the volatility clustering patterns observed over space. The model consists of a log-volatility equation that includes the high-order spatial lags of the log-volatility term and the squared outcome variable. We use a transformation approach to turn the model into a mixture of normals model, and then introduce a Bayesian Markov chain Monte Carlo (MCMC) estimation approach coupled with a data-augmentation technique. Our simulation results show that the Bayesian estimator has good finite sample properties. We apply a first-order version of the spatial GARCH model to US house price returns at the metropolitan statistical area level over the period 2006Q1–2013Q4 and show that there is significant variation in the log-volatility estimates over space in each period.