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The t Copula and Related Copulas
Author(s) -
Demarta Stefano,
McNeil Alexander J.
Publication year - 2005
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2005.tb00254.x
Subject(s) - copula (linguistics) , mathematics , gumbel distribution , bivariate analysis , generalized extreme value distribution , extreme value theory , gaussian , joint probability distribution , tail dependence , maxima , econometrics , combinatorics , statistics , multivariate statistics , physics , art , quantum mechanics , performance art , art history
Summary 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.