A New Multivariate Student-t Distribution with Arbitrary Marginals and its Applications in Financial Time Series

Abstract

A New Multivariate Student-t?Distribution with Arbitrary Marginals and its Applications in Financial Time Series Boris Choy1 1Business School, The University of Sydney, Australia ?:? The conventional multivariate?t-distribution requires its marginal distributions to have the same degrees of freedom and this restriction may not be realistic in many real applications. A new multivariate Student-t?type distribution is therefore proposed. The construction of the distribution is via the mean-variance mixtures. The proposed distribution allows its marginal distributions to have different degrees of freedom. Although the proposed distribution is not elliptical, it is close to elliptical when the marginal degrees of freedom are moderate large and the pair-wise correlations can be easily derived. In the bivariate case, the PDF has a closed form. To demonstrate the superiority of the proposed multivariate?t-distribution to the conventional multivariate?t-distribution, we use a GARCH model with dynamic conditional correlation and a stochastic volatility model with leverage.? Since the construction of the modified?t-distribution is based on the scale mixture of normal (SMN) form of the?t-distribution, the scale mixture variable, the by-product of the SMN form, can be used as a global diagnostic for outliers and the models can be easily implemented using the WinBUGS package. ?