Properties of hierarchical Archimedean copulas

被引：29

作者：

Okhrin, Ostap ^{[1
]}

Okhrin, Yarema ^{[2
]}

Schmid, Wolfgang ^{[3
]}

机构：

[1] Humboldt Univ, Inst Stat & Econometr, D-10099 Berlin, Germany

[2] Univ Augsburg, Dept Stat, D-86135 Augsburg, Germany

[3] European Univ Viadrina, Dept Stat, D-15230 Frankfurt, Oder, Germany

来源：

STATISTICS & RISK MODELING | 2013年 / 30卷 / 01期

关键词：

copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula;

D O I：

10.1524/strm.2013.1071

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula values, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures, and extreme value copulas. We pay special attention to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.

引用

页码：21 / 53

页数：33

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