Hierarchical Archimax copulas

License
http://creativecommons.org/licenses/by-nc-nd/4.0/

Type
Article

Authors
Hofert, Marius
Huser, Raphaël
Prasad, Avinash

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program

Preprint Posting Date
2017-07-03

Online Publication Date
2018-05-16

Print Publication Date
2018-09

Date
2018-05-16

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.

Citation
Hofert M, Huser R, Prasad A (2018) Hierarchical Archimax copulas. Journal of Multivariate Analysis 167: 195–211. Available: http://dx.doi.org/10.1016/j.jmva.2018.05.001.

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.

Publisher
Elsevier BV

Journal
Journal of Multivariate Analysis

DOI
10.1016/j.jmva.2018.05.001

arXiv
1707.00517

Additional Links
http://www.sciencedirect.com/science/article/pii/S0047259X17304074

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