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Hierarchical Archimax copulas

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  • Hofert, Marius
  • Huser, Raphaël
  • Prasad, Avinash

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.

Suggested Citation

  • Hofert, Marius & Huser, Raphaël & Prasad, Avinash, 2018. "Hierarchical Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 195-211.
    • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:195-211
    DOI: 10.1016/j.jmva.2018.05.001
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    References listed on IDEAS

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    6. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
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    2. Mai, Jan-Frederik & Wang, Ruodu, 2021. "Stochastic decomposition for ℓp-norm symmetric survival functions on the positive orthant," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Savinov, Evgeniy & Shamraeva, Victoria, 2023. "On a Rosenblatt-type transformation of multivariate copulas," Econometrics and Statistics, Elsevier, vol. 25(C), pages 39-48.

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