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Nonparametric estimation of pair-copula constructions with the empirical pair-copula

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  • Hobæk Haff, Ingrid
  • Segers, Johan

Abstract

A pair-copula construction is a decomposition of a multivariate copula into a structured system, called regular vine, of bivariate copulae or pair-copulae. The standard practice is to model these pair-copulae parametrically, inducing a model risk, with errors potentially propagating throughout the vine structure. The empirical pair-copula provides a nonparametric alternative, which is conjectured to still achieve the parametric convergence rate. Its main advantage for the user is that it does not require the choice of parametric models for each of the pair-copulae constituting the construction. It can be used as a basis for inference on dependence measures, for selecting an appropriate vine structure, and for testing for conditional independence.

Suggested Citation

  • Hobæk Haff, Ingrid & Segers, Johan, 2015. "Nonparametric estimation of pair-copula constructions with the empirical pair-copula," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 1-13.
    • Handle: RePEc:eee:csdana:v:84:y:2015:i:c:p:1-13
    DOI: 10.1016/j.csda.2014.10.020
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    References listed on IDEAS

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    1. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
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    4. Kjersti Aas & Daniel Berg, 2009. "Models for construction of multivariate dependence - a comparison study," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 639-659.
    5. Bücher, Axel & Dette, Holger, 2010. "A note on bootstrap approximations for the empirical copula process," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1925-1932, December.
    6. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    7. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    9. Brechmann, Eike Christian & Schepsmeier, Ulf, 2013. "Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i03).
    10. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
    11. Aleksey Min & Claudia Czado, 2010. "Bayesian Inference for Multivariate Copulas Using Pair-Copula Constructions," Journal of Financial Econometrics, Oxford University Press, vol. 8(4), pages 511-546, Fall.
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    Cited by:

    1. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    2. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    3. Weiß, Gregor N.F. & Scheffer, Marcus, 2015. "Mixture pair-copula-constructions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 175-191.
    4. Portier, François & Segers, Johan, 2018. "On the weak convergence of the empirical conditional copula under a simplifying assumption," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 160-181.
    5. Cyprian Omari & Peter Mwita & Anthony Waititu, 2019. "Conditional Dependence Modelling with Regular Vine Copulas," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(1), pages 1-5.
    6. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo & Lacal, Virginia, 2016. "Structure learning in Bayesian Networks using regular vines," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 186-208.
    7. Nagler Thomas & Schellhase Christian & Czado Claudia, 2017. "Nonparametric estimation of simplified vine copula models: comparison of methods," Dependence Modeling, De Gruyter, vol. 5(1), pages 99-120, January.
    8. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    9. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, vol. 4(4), pages 1-15, October.
    10. Acar, Elif F. & Czado, Claudia & Lysy, Martin, 2019. "Flexible dynamic vine copula models for multivariate time series data," Econometrics and Statistics, Elsevier, vol. 12(C), pages 181-197.

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