Hierarchical Archimax copulas

Marius Hofert; Raphaël Huser; Avinash Prasad

doi:10.1016/j.jmva.2018.05.001

Hierarchical Archimax copulas

Marius Hofert, Raphaël Huser, Avinash Prasad

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The class of Archimax copulas is generalized to hierarchical Archimax copulas in two ways. First, a hierarchical construction of d-norm generators is introduced to construct hierarchical stable tail dependence functions which induce a hierarchical structure on Archimax copulas. Second, by itself or additionally, hierarchical frailties are introduced to extend Archimax copulas to hierarchical Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Possible extensions to nested Archimax copulas are discussed. A general formula for the density and its evaluation of Archimax copulas is also introduced.

Original language	English (US)
Pages (from-to)	195-211
Number of pages	17
Journal	Journal of Multivariate Analysis
Volume	167
DOIs	https://doi.org/10.1016/j.jmva.2018.05.001
State	Published - May 16 2018

Bibliographical note

KAUST Repository Item: Exported on 2021-02-23
Acknowledgements: The first author acknowledges support from NSERC (Grant RGPIN-5010-2015) and FIM, ETH Zürich. The third author acknowledges support from NSERC (PGS D scholarship). We would also like to thank the Editor-in-Chief, Christian Genest, the Associate Editor and the reviewers for their comments which helped to improve the paper substantially.

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10.1016/j.jmva.2018.05.001

https://repository.kaust.edu.sa/bitstream/10754/626526/6/2018_Hofert-etal_JMVA.pdf

Cite this

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title = "Hierarchical Archimax copulas",

abstract = "The class of Archimax copulas is generalized to hierarchical Archimax copulas in two ways. First, a hierarchical construction of d-norm generators is introduced to construct hierarchical stable tail dependence functions which induce a hierarchical structure on Archimax copulas. Second, by itself or additionally, hierarchical frailties are introduced to extend Archimax copulas to hierarchical Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Possible extensions to nested Archimax copulas are discussed. A general formula for the density and its evaluation of Archimax copulas is also introduced.",

author = "Marius Hofert and Rapha{\"e}l Huser and Avinash Prasad",

note = "KAUST Repository Item: Exported on 2021-02-23 Acknowledgements: The first author acknowledges support from NSERC (Grant RGPIN-5010-2015) and FIM, ETH Z{\"u}rich. The third author acknowledges support from NSERC (PGS D scholarship). We would also like to thank the Editor-in-Chief, Christian Genest, the Associate Editor and the reviewers for their comments which helped to improve the paper substantially.",

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month = may,

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doi = "10.1016/j.jmva.2018.05.001",

language = "English (US)",

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AU - Huser, Raphaël

AU - Prasad, Avinash

N1 - KAUST Repository Item: Exported on 2021-02-23 Acknowledgements: The first author acknowledges support from NSERC (Grant RGPIN-5010-2015) and FIM, ETH Zürich. The third author acknowledges support from NSERC (PGS D scholarship). We would also like to thank the Editor-in-Chief, Christian Genest, the Associate Editor and the reviewers for their comments which helped to improve the paper substantially.

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Y1 - 2018/5/16

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AB - The class of Archimax copulas is generalized to hierarchical Archimax copulas in two ways. First, a hierarchical construction of d-norm generators is introduced to construct hierarchical stable tail dependence functions which induce a hierarchical structure on Archimax copulas. Second, by itself or additionally, hierarchical frailties are introduced to extend Archimax copulas to hierarchical Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Possible extensions to nested Archimax copulas are discussed. A general formula for the density and its evaluation of Archimax copulas is also introduced.

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JO - Journal of Multivariate Analysis

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SN - 0047-259X

ER -

Hierarchical Archimax copulas

Abstract

Bibliographical note

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