Bayesian Inference for Spatial Stochastic Volatility Models ∗

In this study, we propose a spatial stochastic volatility model in which the latent log-volatility terms follow a spatial autoregressive process. Though there is no spatial correlation in the outcome equation (the mean equation), the spatial autoregressive process defined for the log-volatility terms introduces spatial dependence in the outcome equation. To introduce a Bayesian Markov chain Monte Carlo (MCMC) estimation algorithm, we transform the model so that the outcome equation takes the form of log-squared terms. We approximate the distribution of the log-squared error terms in the outcome equation with a finite mixture of normal distributions so that the transformed model turns into a linear Gaussian state-space model. Our simulation results indicate that the Bayesian estimator has satisfactory finite sample properties. We investigate the practical usefulness of our proposed model and estimation method by using the price returns of residential properties in the broader Chicago Metropolitan area. Bayesian estimator the Gaussian mixture approximation has good finite sample properties. In an empirical application using the price returns in the residential properties in the of and its we showed that although there is weak positive spatial correlation in the but a strong positive spatial correlation in log-volatility terms. Our results on the estimated conditional variances indicated that the lowest estimates are over of of while relatively larger estimates are distributed over a corridor extending from the west side of city to the south side.