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Multivariate conditional versions of Spearman's rho and related measures of tail dependence

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  • Schmid, Friedrich
  • Schmidt, Rafael

Abstract

A new family of conditional-dependence measures based on Spearman's rho is introduced. The corresponding multidimensional versions are established. Asymptotic distributional results are derived for related estimators which are based on the empirical copula. Particular emphasis is placed on a new type of multidimensional tail-dependence measure and its relationship to other measures of tail dependence is shown. Multivariate tail dependence describes the limiting amount of dependence in the vertices of the copula's domain.

Suggested Citation

  • Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1123-1140
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    References listed on IDEAS

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    1. Rafael Schmidt & Ulrich Stadtmüller, 2006. "Non-parametric Estimation of Tail Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, pages 307-335.
    2. Kristin J. Forbes & Roberto Rigobon, 2002. "No Contagion, Only Interdependence: Measuring Stock Market Comovements," Journal of Finance, American Finance Association, vol. 57(5), pages 2223-2261, October.
    3. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, pages 12-30.
    4. Schlather, Martin, 2001. "Examples for the coefficient of tail dependence and the domain of attraction of a bivariate extreme value distribution," Statistics & Probability Letters, Elsevier, pages 325-329.
    5. Campbell, Rachel & Koedijk, Kees & Kofman, Paul, 2002. "Increased Correlation in Bear markets: A Downside Risk Perspective," CEPR Discussion Papers 3172, C.E.P.R. Discussion Papers.
    6. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), pages 301-327.
    7. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, pages 80-100.
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    Citations

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    Cited by:

    1. Ferreira, H., 2011. "Dependence between two multivariate extremes," Statistics & Probability Letters, Elsevier, pages 586-591.
    2. Ferreira, Helena & Ferreira, Marta, 2012. "Tail dependence between order statistics," Journal of Multivariate Analysis, Elsevier, pages 176-192.
    3. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    4. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    5. Klein, Ingo & Tinkl, Fabian, 2011. "Some critical remarks on Zhang's gamma test for independence," Discussion Papers 87/2010, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    6. Gaißer, Sandra & Schmid, Friedrich, 2010. "On testing equality of pairwise rank correlations in a multivariate random vector," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2598-2615, November.
    7. Carl S. Bonham & Peter Fuleky & Qianxue Zhao, 2013. "Estimating Demand Elasticities in Non-Stationary Panels: The Case of Hawaii's Tourism Industry," Working Papers 201303, University of Hawaii at Manoa, Department of Economics.
    8. Furman, Edward & Kuznetsov, Alexey & Su, Jianxi & Zitikis, Ričardas, 2016. "Tail dependence of the Gaussian copula revisited," Insurance: Mathematics and Economics, Elsevier, pages 97-103.
    9. Fung, Thomas & Seneta, Eugene, 2011. "The bivariate normal copula function is regularly varying," Statistics & Probability Letters, Elsevier, pages 1670-1676.
    10. Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.
    11. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    12. Gaißer, Sandra & Ruppert, Martin & Schmid, Friedrich, 2010. "A multivariate version of Hoeffding's Phi-Square," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2571-2586, November.
    13. Liu, Ming & La Croix, Sumner, 2015. "A cross-country index of intellectual property rights in pharmaceutical inventions," Research Policy, Elsevier, pages 206-216.
    14. Ming Liu & Sumner La Croix, 2014. "A Cross-Country Index of Intellectual Property Rights in Pharmaceutical Innovations," Working Papers 201408, University of Hawaii at Manoa, Department of Economics.
    15. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2014. "Clustering of financial time series in risky scenarios," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(4), pages 359-376, December.
    16. Christian Koziol & Philipp Koziol & Thomas Schön, 2015. "Do correlated defaults matter for CDS premia? An empirical analysis," Review of Derivatives Research, Springer, vol. 18(3), pages 191-224, October.
    17. Philipp Matros & Johannes Vilsmeier, 2013. "The Multivariate Option iPoD Framework - Assessing Systemic Financial Risk," Working Papers 143, Bavarian Graduate Program in Economics (BGPE).
    18. Melanie Frick, 2012. "Measures of multivariate asymptotic dependence and their relation to spectral expansions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, pages 819-831.
    19. Bücher Axel, 2014. "A note on nonparametric estimation of bivariate tail dependence," Statistics & Risk Modeling, De Gruyter, pages 1-12.
    20. Nadarajah, Saralees, 2015. "Expansions for bivariate copulas," Statistics & Probability Letters, Elsevier, pages 77-84.
    21. Ming Liu & Sumner la Croix, 2013. "A Cross-Country Index of Intellectual Property Rights in Pharmaceutical Innovations," Working Papers 201313, University of Hawaii at Manoa, Department of Economics.
    22. repec:eee:insuma:v:74:y:2017:i:c:p:109-121 is not listed on IDEAS

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