The t Copula and Related Copulas

2007/01/15 by Stefano Demarta, Alexander J. McNeil · 28 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Statistical Distribution Estimation and Applications

paper · doi:10.1111/j.1751-5823.2005.tb00254.x

openalex publication_date 2007/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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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