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Nonparametric estimation of the lower tail dependence λL in bivariate copulas

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  • Jadran Dobric
  • Friedrich Schmid

Abstract

The lower tail dependence λL is a measure that characterizes the tendency of extreme co-movements in the lower tails of a bivariate distribution. It is invariant with respect to strictly increasing transformations of the marginal distribution and is therefore a function of the copula of the bivariate distribution. λL plays an important role in modelling aggregate financial risk with copulas. This paper introduces three non-parametric estimators for λL. They are weakly consistent under mild regularity conditions on the copula and under the assumption that the number k = k(n) of observations in the lower tail, used for estimation, is asymptotically k ≈ √n. The finite sample properties of the estimators are investigated using a Monte Carlo simulation in special cases. It turns out that these estimators are biased, where amount and sign of the bias depend on the underlying copula, on the sample size n, on k, and on the true value of λL.

Suggested Citation

  • Jadran Dobric & Friedrich Schmid, 2005. "Nonparametric estimation of the lower tail dependence λL in bivariate copulas," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(4), pages 387-407.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:4:p:387-407
    DOI: 10.1080/02664760500079217
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    References listed on IDEAS

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    1. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
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    Cited by:

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    8. Dominique Guegan & Giovanni De Luca & Giorgia Rivieccio, 2017. "Three-stage estimation method for non-linear multiple time-series," Documents de travail du Centre d'Economie de la Sorbonne 17001, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Luca, Giovanni De & Guégan, Dominique & Rivieccio, Giorgia, 2019. "Assessing tail risk for nonlinear dependence of MSCI sector indices: A copula three-stage approach," Finance Research Letters, Elsevier, vol. 30(C), pages 327-333.
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    11. Dominique Guegan & Giovanni de Luca & Giorgia Rivieccio, 2017. "Three-stage estimation method for non-linear multiple time-series," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01439860, HAL.
    12. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    13. Fousekis, Panos & Grigoriadis, Vasilis, 2016. "Spatial price dependence by time scale: Empirical evidence from the international butter markets," Economic Modelling, Elsevier, vol. 54(C), pages 195-204.
    14. Chen, Zhongfei & Wanke, Peter & Antunes, Jorge Junio Moreira & Zhang, Ning, 2017. "Chinese airline efficiency under CO2 emissions and flight delays: A stochastic network DEA model," Energy Economics, Elsevier, vol. 68(C), pages 89-108.
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    16. Fischer, Matthias J. & Hinzmann, Gerd, 2006. "A new class of copulas with tail dependence and a generalized tail dependence estimator," Discussion Papers 77/2006, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.

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