Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula

An objective Bayesian approach to estimate the number of degrees of freedom (nu) for the multivariate t distribution and for the t-copula, when the parameter is considered discrete, is proposed. Inference on this parameter has been problematic for the multivariate t and, for the absence of any method, for the t-copula. An objective criterion based on loss functions which allows to overcome the issue of defining objective probabilities directly is employed. The support of the prior for nu is truncated, which derives from the property of both the multivariate t and the t-copula of convergence to normality for a sufficiently large number of degrees of freedom. The performance of the priors is tested on simulated scenarios. The R codes and the replication material are available as a supplementary material of the electronic version of the paper and on real data: daily logarithmic returns of IBM and of the Center for Research in Security Prices Database.