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Tails of correlation mixtures of elliptical copulas

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  • Manner, Hans
  • Segers, Johan

Abstract

Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Student t-copulas, tail dependence at sub-asymptotic levels is generally larger than in the limit, which can have serious consequences for estimation and evaluation of extreme risk. Finally, although correlation mixtures of Gaussian copulas inherit the property of asymptotic independence, at the same time they fall in the newly defined category of near asymptotic dependence. The consequences of these findings for modeling are assessed by means of a simulation study and a case study involving financial time series.

Suggested Citation

  • Manner, Hans & Segers, Johan, 2011. "Tails of correlation mixtures of elliptical copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 153-160, January.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:153-160
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Krenar AVDULAJ & Jozef BARUNIK, 2013. "Can We Still Benefit from International Diversification? The Case of the Czech and German Stock Markets," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(5), pages 425-442, November.
    2. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    3. Yang, Yang & Hashorva, Enkelejd, 2013. "Extremes and products of multivariate AC-product risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 312-319.
    4. Fabrizio Durante & Ostap Okhrin, 2014. "Estimation procedures for exchangeable Marshall copulas with hydrological application," SFB 649 Discussion Papers SFB649DP2014-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Fung, Thomas & Seneta, Eugene, 2014. "Convergence rate to a lower tail dependence coefficient of a skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 62-72.
    6. Liu, Aiai & Hou, Yanxi & Peng, Liang, 2015. "Interval estimation for a measure of tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 294-305.
    7. repec:bla:jrinsu:v:84:y:2017:i:s1:p:393-415 is not listed on IDEAS
    8. Avdulaj, Krenar & Barunik, Jozef, 2015. "Are benefits from oil–stocks diversification gone? New evidence from a dynamic copula and high frequency data," Energy Economics, Elsevier, vol. 51(C), pages 31-44.
    9. Fung, Thomas & Seneta, Eugene, 2016. "Tail asymptotics for the bivariate skew normal," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 129-138.
    10. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    11. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, Elsevier.
    12. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.

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