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

Villa, Cristiano, Rubio, Francisco J. (2018) Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula. Computational Statistics and Data Analysis, 124 . pp. 197-217. ISSN 0167-9473. (doi:10.1016/j.csda.2018.03.010)

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## Abstract

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 and on real data: daily logarithmic returns of IBM and of the Center for Research in Security Prices Database.

Item Type: Article 10.1016/j.csda.2018.03.010 [UNSPECIFIED] Bayesian methods in support of risk management and asset pricing of large stock portfolios. Information loss; Kullback–Leibler divergence; Log-returns; Multivariate t distribution; Objective prior; t-copula Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics Cristiano Villa 27 Mar 2018 11:13 UTC 16 Aug 2019 15:31 UTC https://kar.kent.ac.uk/id/eprint/66547 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-2670-2954