An Application of Bayesian Seemingly Unrelated Regression Models with Flexible Tails

Seemingly unrelated regression (SUR) models are useful for capturing the correlation structure between different regression equations. While the multivariate normal distribution is a common choice for the random error term in an SUR model, the multivariate t-distribution is also popular for robustness considerations. However, the multivariate t-distribution is elliptical which leads to the limitation that the degrees of freedom of its marginal distributions are identical. In this paper, we consider a non-elliptical multivariate Student-t error distribution which allows flexible shape parameters for the marginal distributions. This non-elliptical distribution is constructed via a scale mixtures of normal form and therefore the Markov chain Monte Carlo (MCMC) algorithms are used for Bayesian inference of SUR models. In the empirical study of the capital asset pricing model (CAPM), we show that this non-elliptical Student-t distribution outperforms the multivariate normal and multivariate Student-t distributions.