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Kendall’s tau and agglomerative clustering for structure determination of hierarchical Archimedean copulas

Author

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  • Górecki J.

    (Department of Informatics, SBA in Karviná, Silesian University in Opava, Univerzitní námestí 1934/3, 733 40 Karviná, Czech Republic)

  • Hofert M.

    (Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada)

  • Holeňa M.

    (Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou veží 271/2, 182 07 Praha, Czech Republic)

Abstract

Several successful approaches to structure determination of hierarchical Archimedean copulas (HACs) proposed in the literature rely on agglomerative clustering and Kendall’s correlation coefficient. However, there has not been presented any theoretical proof justifying such approaches. This work fills this gap and introduces a theorem showing that, given the matrix of the pairwise Kendall correlation coefficients corresponding to a HAC, its structure can be recovered by an agglomerative clustering technique.

Suggested Citation

  • Górecki J. & Hofert M. & Holeňa M., 2017. "Kendall’s tau and agglomerative clustering for structure determination of hierarchical Archimedean copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 75-87, January.
    • Handle: RePEc:vrs:demode:v:5:y:2017:i:1:p:75-87:n:5
    DOI: 10.1515/demo-2017-0005
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    References listed on IDEAS

    as
    1. Segers, Johan & Uyttendaele, Nathan, 2014. "Nonparametric estimation of the tree structure of a nested Archimedean copula," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 190-204.
    2. Rezapour, Mohsen, 2015. "On the construction of nested Archimedean copulas for d-monotone generators," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 21-32.
    3. Hofert, Marius, 2011. "Efficiently sampling nested Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 57-70, January.
    4. Matsypura, Dmytro & Neo, Emily & Prokhorov, Artem, 2016. "Estimation of Hierarchical Archimedean Copulas as a Shortest Path Problem," Economics Letters, Elsevier, vol. 149(C), pages 131-134.
    5. Uyttendaele, Nathan, 2016. "On the estimation of nested Archimedean copulas: A theoretical and an experimental comparison," LIDAM Discussion Papers ISBA 2016005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Zhu, Wenjun & Wang, Chou-Wen & Tan, Ken Seng, 2016. "Structure and estimation of Lévy subordinated hierarchical Archimedean copulas (LSHAC): Theory and empirical tests," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 20-36.
    7. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, vol. 173(2), pages 189-204.
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