The t Copula and Related Copulas

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The t Copula and Related Copulas

by Stefano Demarta of ETH Zentrum, and
Alexander J. McNeil of ETH Zentrum

May 2004

Abstract: The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively.

Published in: International Statistical Review, Vol. 73, No. 1, (April 2005), pp. 111-129.

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