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.
| Original language | English |
|---|---|
| Pages (from-to) | 111-129 |
| Number of pages | 19 |
| Journal | International Statistical Review |
| Volume | 73 |
| Issue number | 1 |
| Publication status | Published - Apr 2005 |
Keywords
- Clayton copula
- Copula
- Gumbel copula
- Kendall's rank correlation
- Multivariate extreme value theory
- Multivariate t distribution
- Tail dependence