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A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models

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Krajina, A. (Tilburg University, Center for Economic Research)

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Abstract

An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correla- tion parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by J.H.J. Einmahl, A. Krajina and J. Segers [Bernoulli 14(4), 2008, 1003-1026]. We show that such an estimator is consistent and asymptotically normal. Also, we derive the joint limit distribution of the estimators of the two parameters. By a simulation study, we illustrate the small sample behavior of the estimator of the tail parameter and we compare its performance to that of the estimator proposed in the paper by C. KlÄuppelberg, G. Kuhn and L. Peng [Scandinavian Journal of Statistics 35(4), 2008, 701-718].

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2009-42.

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Date of creation: 2009
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Handle: RePEc:dgr:kubcen:200942

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions

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  1. Asimit, Alexandru V. & Jones, Bruce L., 2007. "Extreme behavior of bivariate elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 53-61, July. [Downloadable!] (restricted)
  2. Hashorva, Enkelejd, 2005. "Extremes of asymptotically spherical and elliptical random vectors," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 285-302, June. [Downloadable!] (restricted)
  3. Einmahl, J.H.J. & Haan, L. de & Li, D., 2004. "Weighted approximations of tail copula processes with application to testing the multivariate extreme value condition," Discussion Paper 71, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Claudia Klüppelberg & Gabriel Kuhn & Liang Peng, 2008. "Semi-Parametric Models for the Multivariate Tail Dependence Function - the Asymptotically Dependent Case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 35(4), pages 701-718. [Downloadable!] (restricted)
  5. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
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