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X-Vine Models for Multivariate Extremes

Author

Listed:
  • Kiriliouk, Anna

    (Université de Namur)

  • Lee, Jeongjin

    (Université de Namur)

  • Segers, Johan

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

Regular vine sequences permit the organisation of variables in a random vector along a sequence of trees. Regular vine models have become greatly popular in dependence modelling as a way to combine arbitrary bivariate copulas into higher-dimensional ones, offering flexibility, parsimony, and tractability. In this project, we use regular vine structures to decompose and construct the exponent measure density of a multivariate extreme value distribution, or, equivalently, the tail copula density. Although these densities pose theoretical challenges due to their infinite mass, their homogeneity property offers simplifications. The theory sheds new light on existing parametric families and facilitates the construction of new ones, called X-vines. Computations proceed via recursive formulas in terms of bivariate model components. We develop simulation algorithms for X-vine multivariate Pareto distributions as well as methods for parameter estimation and model selection on the basis of threshold exceedances. The methods are illustrated by Monte Carlo experiments and a case study on US flight delay data.

Suggested Citation

  • Kiriliouk, Anna & Lee, Jeongjin & Segers, Johan, 2023. "X-Vine Models for Multivariate Extremes," LIDAM Discussion Papers ISBA 2023038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2023038
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    References listed on IDEAS

    as
    1. Einmahl, John & Kiriliouk, A. & Segers, J.J.J., 2016. "A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions," Other publications TiSEM a3e7350b-4773-4bd8-9c3c-6, Tilburg University, School of Economics and Management.
    2. Einmahl, J.H.J. & Krajina, A. & Segers, J.J.J., 2007. "A Method of Moments Estimator of Tail Dependence," Discussion Paper 2007-80, Tilburg University, Center for Economic Research.
    3. Hu, Shuang & Peng, Zuoxiang & Segers, Johan, 2023. "Modeling multivariate extreme value distributions via Markov trees," LIDAM Reprints ISBA 2023031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Rafael Schmidt & Ulrich Stadtmüller, 2006. "Non‐parametric Estimation of Tail Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 307-335, June.
    5. de Haan, Laurens & Neves, Cláudia & Peng, Liang, 2008. "Parametric tail copula estimation and model testing," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1260-1275, July.
    6. Sebastian Engelke & Stanislav Volgushev, 2022. "Structure learning for extremal tree models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 2055-2087, November.
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