Bayesian Inference in Spatial Stochastic Volatility Models with An Application to House Price Returns in Chicago (Under Review)

In this study, we consider a spatial stochastic volatility model in which the latent log-volatility term is specified through 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 term introduces spatial dependence in the outcome equation. To introduce the Bayesian Markov chain Monte Carlo (MCMC) estimation approach, we transform the model such that the outcome equation is in the form of log-squared terms. We approximate the distribution of the log-squared error term in the outcome equation with a finite mixture of normal distributions such that the transformed model turns into a linear Gaussian state-space model, where the log-volatility equation constitutes the state equation. We develop an MCMC algorithm in which the latent log-volatility term is considered as an additional parameter to facilitate the posterior simulation. Our simulation results indicate that the Bayesian estimator has satisfactory finite sample properties. We investigate the empirical validity of our specification by using the price returns of residential properties in the broader Chicago area for the years 2014 and 2015.