The t Copula and Related Copulas |
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Authors: | Stefano Demarta Alexander J McNeil |
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Institution: | Department of Mathematics, Federal Institute of Technology, ETH Zentrum, CH-8092 Zürich, Switzerland. E-mail: |
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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. |
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Keywords: | Copula Multivariate t distribution Kendall's rank correlation Tail dependence Multivariate extreme value theory Gumbel copula Clayton copula |
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