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A note on upper-patched generators for Archimedean copulas

Author

Listed:
  • Elena Di Bernardino

    (CEDRIC - MSDMA - CEDRIC. Méthodes statistiques de data-mining et apprentissage - CEDRIC - Centre d'études et de recherche en informatique et communications - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - CNAM - Conservatoire National des Arts et Métiers [CNAM] - HESAM - HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université)

  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

The class of multivariate Archimedean copulas is defined by using a real-valued function called the generator of the copula. This generator satisfies some properties, including d-monotony. We propose here a new basic transformation of this generator, preserving these properties, thus ensuring the validity of the transformed generator and inducing a proper valid copula. This transformation acts only on a specific portion of the generator, it allows both the non-reduction of the likelihood on a given dataset, and the choice of the upper tail dependence coefficient of the transformed copula. Numerical illustrations show the utility of this construction, which can improve the fit of a given copula both on its central part and its tail.

Suggested Citation

  • Elena Di Bernardino & Didier Rullière, 2017. "A note on upper-patched generators for Archimedean copulas," Post-Print hal-01347869, HAL.
    • Handle: RePEc:hal:journl:hal-01347869
    DOI: 10.1051/ps/2017003
    Note: View the original document on HAL open archive server: https://hal.science/hal-01347869v2
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    References listed on IDEAS

    as
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    12. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
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    18. Aulbach, Stefan & Falk, Michael & Hofmann, Martin, 2012. "The multivariate Piecing-Together approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 161-170.
    19. Elena Di Bernardino & Didier Rullière, 2015. "Estimation of multivariate critical layers: Applications to rainfall data," Post-Print hal-00940089, HAL.
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    Cited by:

    1. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    2. Moshe Kelner & Zinoviy Landsman & Udi E. Makov, 2021. "Compound Archimedean Copulas," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 126-126, June.
    3. Fousekis, Panos & Grigoriadis, Vasilis, 2017. "Price co-movement and the crack spread in the US futures markets," Journal of Commodity Markets, Elsevier, vol. 7(C), pages 57-71.
    4. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.

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    Keywords

    Archimedean copulas; transformations; distortions; tail dependence coefficients; likelihood;
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