Bayesian Estimation of Unknown Heteroscedastic Variances

We propose a Bayesian procedure to estimate possibly heteroscedastic variances of the regression error term, without assuming any structure on them. What we propose in this paper, may be construed as a Conditional Bayesian procedure that is conditioned upon the HCCM obtained from the OLS estimation of the original regression model. After we obtain the Eicker-White HCCM, we set up a Bayesian model and use an MCMC to simulate posterior pdf's of heteroscedastic variances whose structures are unknown. In addition to the numerical examples, we present an empirical investigation on the stock prices of Japanese pharmaceutical and biomedical companies.