Multivariate Archimax copulas

A. Charpentier; A. L. Fougères; C. Genest; J. G. Nešlehová

doi:10.1016/j.jmva.2013.12.013

Multivariate Archimax copulas

A. Charpentier, A. L. Fougères, C. Genest^*, J. G. Nešlehová

^*Corresponding author for this work

Publication: Scientific journal › Journal article › peer-review

Abstract

A multivariate extension of the bivariate class of Archimax copulas was recently proposed by Mesiar and Jágr (2013), who asked under which conditions it holds. This paper answers their question and provides a stochastic representation of multivariate Archimax copulas. A few basic properties of these copulas are explored, including their minimum and maximum domains of attraction. Several non-trivial examples of multivariate Archimax copulas are also provided.

Original language	English
Pages (from-to)	118-136
Number of pages	19
Journal	Journal of Multivariate Analysis
Volume	126
DOIs	https://doi.org/10.1016/j.jmva.2013.12.013
Publication status	Published - Apr 2014
Externally published	Yes

Bibliographical note

Funding Information:
Most of this work was carried out while Genest and Nešlehová were visiting the Université Claude-Bernard in Lyon; they are grateful to the members of the Institut Camille Jordan for their hospitality. This research was supported by the LABEX MILYON ( ANR–10–LABX–0070 ) of Université de Lyon, within the program “Investissements d’avenir” (ANR–11–IDEX–0007) operated by the Agence nationale pour la recherche. Additional funding for this work was provided by the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada , and the Fonds de recherche du Québec–Nature et technologies .

Keywords

Archimedean copula
Domain of attraction
Multivariate extreme-value distribution
Stable tail dependence function
Williamson d-transform

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title = "Multivariate Archimax copulas",

abstract = "A multivariate extension of the bivariate class of Archimax copulas was recently proposed by Mesiar and J{\'a}gr (2013), who asked under which conditions it holds. This paper answers their question and provides a stochastic representation of multivariate Archimax copulas. A few basic properties of these copulas are explored, including their minimum and maximum domains of attraction. Several non-trivial examples of multivariate Archimax copulas are also provided.",

keywords = "Archimedean copula, Domain of attraction, Multivariate extreme-value distribution, Stable tail dependence function, Williamson d-transform",

author = "A. Charpentier and Foug{\`e}res, {A. L.} and C. Genest and Ne{\v s}lehov{\'a}, {J. G.}",

note = "Funding Information: Most of this work was carried out while Genest and Ne{\v s}lehov{\'a} were visiting the Universit{\'e} Claude-Bernard in Lyon; they are grateful to the members of the Institut Camille Jordan for their hospitality. This research was supported by the LABEX MILYON ( ANR–10–LABX–0070 ) of Universit{\'e} de Lyon, within the program “Investissements d{\textquoteright}avenir” (ANR–11–IDEX–0007) operated by the Agence nationale pour la recherche. Additional funding for this work was provided by the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada , and the Fonds de recherche du Qu{\'e}bec–Nature et technologies . ",

year = "2014",

month = apr,

doi = "10.1016/j.jmva.2013.12.013",

language = "English",

volume = "126",

pages = "118--136",

journal = "Journal of Multivariate Analysis",

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AU - Fougères, A. L.

AU - Genest, C.

AU - Nešlehová, J. G.

N1 - Funding Information: Most of this work was carried out while Genest and Nešlehová were visiting the Université Claude-Bernard in Lyon; they are grateful to the members of the Institut Camille Jordan for their hospitality. This research was supported by the LABEX MILYON ( ANR–10–LABX–0070 ) of Université de Lyon, within the program “Investissements d’avenir” (ANR–11–IDEX–0007) operated by the Agence nationale pour la recherche. Additional funding for this work was provided by the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada , and the Fonds de recherche du Québec–Nature et technologies .

PY - 2014/4

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N2 - A multivariate extension of the bivariate class of Archimax copulas was recently proposed by Mesiar and Jágr (2013), who asked under which conditions it holds. This paper answers their question and provides a stochastic representation of multivariate Archimax copulas. A few basic properties of these copulas are explored, including their minimum and maximum domains of attraction. Several non-trivial examples of multivariate Archimax copulas are also provided.

AB - A multivariate extension of the bivariate class of Archimax copulas was recently proposed by Mesiar and Jágr (2013), who asked under which conditions it holds. This paper answers their question and provides a stochastic representation of multivariate Archimax copulas. A few basic properties of these copulas are explored, including their minimum and maximum domains of attraction. Several non-trivial examples of multivariate Archimax copulas are also provided.

KW - Archimedean copula

KW - Domain of attraction

KW - Multivariate extreme-value distribution

KW - Stable tail dependence function

KW - Williamson d-transform

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U2 - 10.1016/j.jmva.2013.12.013

DO - 10.1016/j.jmva.2013.12.013

M3 - Journal article

AN - SCOPUS:84893925602

SN - 0047-259X

VL - 126

SP - 118

EP - 136

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

ER -

Multivariate Archimax copulas

Abstract

Bibliographical note

Keywords

Access to Document

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