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Multivariate Archimax copulas

Author

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  • Charpentier, A.
  • Fougères, A.-L.
  • Genest, C.
  • Nešlehová, J.G.

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.

Suggested Citation

  • Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    • Handle: RePEc:eee:jmvana:v:126:y:2014:i:c:p:118-136
    DOI: 10.1016/j.jmva.2013.12.013
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    References listed on IDEAS

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    Cited by:

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    2. Mhalla, Linda & Chavez-Demoulin, Valérie & Naveau, Philippe, 2017. "Non-linear models for extremal dependence," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 49-66.
    3. Durante Fabrizio & Sánchez Juan Fernández & Sempi Carlo, 2018. "A note on bivariate Archimax copulas," Dependence Modeling, De Gruyter, vol. 6(1), pages 178-182, October.
    4. Di Bernardino Elena & Rullière Didier, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-20, December.
    5. Zhang, Yi & Gomes, António Topa & Beer, Michael & Neumann, Ingo & Nackenhorst, Udo & Kim, Chul-Woo, 2019. "Reliability analysis with consideration of asymmetrically dependent variables: Discussion and application to geotechnical examples," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 261-277.
    6. 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).
    7. Hofert, Marius, 2021. "Right-truncated Archimedean and related copulas," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 79-91.
    8. Chaoubi, Ihsan & Cossette, Hélène & Marceau, Etienne & Robert, Christian Y., 2021. "Hierarchical copulas with Archimedean blocks and asymmetric between-block pairs," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    9. Sabrina Mulinacci, 2022. "A Marshall-Olkin Type Multivariate Model with Underlying Dependent Shocks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2455-2484, December.
    10. Mai Jan-Frederik, 2022. "About the exact simulation of bivariate (reciprocal) Archimax copulas," Dependence Modeling, De Gruyter, vol. 10(1), pages 29-47, January.
    11. Krupskii, Pavel & Joe, Harry & Lee, David & Genton, Marc G., 2018. "Extreme-value limit of the convolution of exponential and multivariate normal distributions: Link to the Hüsler–Reiß distribution," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 80-95.
    12. Hofert, Marius & Huser, Raphaël & Prasad, Avinash, 2018. "Hierarchical Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 195-211.
    13. Diakarya Barro & Moumouni Diallo & Remi Guillaume Bagré, 2016. "Spatial Tail Dependence and Survival Stability in a Class of Archimedean Copulas," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-8, July.
    14. Elena Di Bernardino & Didier Rullière, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Working Papers hal-01147778, HAL.
    15. Sabrina Mulinacci, 2017. "A systemic shock model for too big to fail financial institutions," Papers 1704.02160, arXiv.org, revised Apr 2017.
    16. Bücher Axel & Jaser Miriam & Min Aleksey, 2021. "Detecting departures from meta-ellipticity for multivariate stationary time series," Dependence Modeling, De Gruyter, vol. 9(1), pages 121-140, January.
    17. Górecki, Jan & Hofert, Marius & Okhrin, Ostap, 2021. "Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    18. Bücher, Axel & Volgushev, Stanislav & Zou, Nan, 2019. "On second order conditions in the multivariate block maxima and peak over threshold method," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 604-619.

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