Bayes prediction in regressions with elliptical errors

In this paper the prediction problem is considered for linear regression models with elliptical errors when the Bayes prior is non-informative. We show that the Bayes prediction density under the elliptical errors assumption is exactly the same as that obtained with normally distributed errors. Thus, assuming that the errors have a normal distribution, when the true distribution is elliptical, will not lead to incorrect predictive inferences if the error variance structure is correctly specified. This extends the results of Zellner (1976). Finally, based on Monte Carlo numerical integration procedures, computations are provided in a model with multiplicative heteroscedasticity.