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.
Publié le : 2005-04-14
Classification:
Copula,
Multivariate t distribution,
Kendall's rank correlation,
Tail dependence,
Multivariate extreme value theory,
Gumbel copula,
Clayton copula
@article{1112304815,
author = {Demarta, Stefano and Mcneil, Alexander J.},
title = {The $t$ Copula and Related Copulas},
journal = {Internat. Statist. Rev.},
volume = {73},
number = {1},
year = {2005},
pages = { 111-129},
language = {en},
url = {http://dml.mathdoc.fr/item/1112304815}
}
Demarta, Stefano; Mcneil, Alexander J. The $t$ Copula and Related Copulas. Internat. Statist. Rev., Tome 73 (2005) no. 1, pp. 111-129. http://gdmltest.u-ga.fr/item/1112304815/