Bayesian treatment of the independent student-t linear model

Abstract

This article takes up methods for Bayesian inference in a linear model in which the disturbances are independent and have identical Student-t distributions. It exploits the equivalence of the Student-t distribution and an appropriate scale mixture of normals, and uses a Gibbs sampler to perform the computations. The new method is applied to some well-known macroeconomic time series. It is found that posterior odds ratios favour the independent Student-t linear model over the normal linear model, and that the posterior odds ratio in favour of difference stationarity over trend stationarity is often substantially less in the favoured Student-t models.