General multivariate dependence using associated copulas

Yuri Salazar Flores*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper studies the general multivariate dependence and tail dependence of a ran- dom vector. We analyse the dependence of variables going up or down, covering the 2d orthants of dimension d and accounting for non-positive dependence. We extend definitions and results from positive to general dependence using the associated cop- ulas. We study several properties of these copulas and present general versions of the tail dependence functions and tail dependence coefficients. We analyse the perfect dependence models, elliptical copulas and Archimedean copulas. We introduce the monotonic copulas and prove that the multivariate Student’s t copula accounts for all types of tail dependence simultaneously while Archimedean copulas with strict generators can only account for positive tail dependence.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalRevstat Statistical Journal
Volume14
Issue number1
Publication statusPublished - 1 Feb 2016

Keywords

  • Archimedean copulas
  • Copula theory
  • Elliptical copulas
  • Non-positive dependence
  • Perfect dependence models
  • Tail dependence

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