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A STATISTICAL METHODOLOGY FOR ASSESSING THE MAXIMAL STRENGTH OF TAIL DEPENDENCE

Published online by Cambridge University Press:  29 June 2020

Ning Sun ,
Chen Yang Open the ORCID record for Chen Yang [Opens in a new window]  and
Ričardas Zitikis
Ning Sun
Affiliation:
School of Mathematical and Statistical Sciences, Western University, London, ONN6A 5B7, Canada
Chen Yang*
Affiliation:
School of Mathematical and Statistical Sciences, Western University, London, ONN6A 5B7, Canada Economics and Management School, Wuhan University, Wuhan, Hubei430072, People’s Republic of China, E-Mail: cyang244@whu.edu.cn
Ričardas Zitikis
Affiliation:
School of Mathematical and Statistical Sciences, Western University, London, ONN6A 5B7, Canada Risk and Insurance Studies Centre, York University, Toronto, ONM3J 1P3, Canada
*
E-Mail: cyang244@whu.edu.cn
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Abstract

Several diagonal-based tail dependence indices have been suggested in the literature to quantify tail dependence. They have well-developed statistical inference theories but tend to underestimate tail dependence. For those problems when assessing the maximal strength of dependence is important (e.g., co-movements of financial instruments), the maximal tail dependence index was introduced, but it has so far lacked empirical estimators and statistical inference results, thus hindering its practical use. In the present paper, we suggest an empirical estimator for the index, explore its statistical properties, and illustrate its performance on simulated data.

Keywords

Copulamaximal tail dependencestatistical estimationKendall’s distribution
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 799 - 825
Copyright
© 2020 by Astin Bulletin. All rights reserved

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References

Basel Committee on Banking Supervision (2016) Minimum Capital Requirements for Market Risk (January, 2016). Bank for International Settlements, Basel. https://www.bis.org/bcbs/publ/d352.htm.Google Scholar
Basel Committee on Banking Supervision (2019) Minimum Capital Requirements for Market Risk (February, 2019). Bank for International Settlements, Basel. https://www.bis.org/bcbs/publ/d457.htm.Google Scholar
Berghaus, B., Bücher, A. and Volgushev, S. (2017) Weak convergence of the empirical copula process with respect to weighted metrics. Bernoulli, 23, 743–772.CrossRefGoogle Scholar
Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987) Regular Variation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Cherubini, U., Luciano, E. and Vecchiato, W. (2013) Copula Methods in Finance. Chichester: Wiley.Google Scholar
Cherubini, U., Durante, F. and Mulinacci, S. (2015) Marshall Olkin Distributions – Advances in Theory and Applications. New York: Springer.CrossRefGoogle Scholar
Coles, S., Heffernan, J. and Tawn, J. (1999) Dependence measures for extreme value analyses. Extremes, 2, 339–365.CrossRefGoogle Scholar
Draisma, G., Drees, H., Ferreira, A. and de Haan, L. (2004) Bivariate tail estimation: dependence in asymptotic independence. Bernoulli, 10, 251–280.CrossRefGoogle Scholar
Durante, F. and Sempi, C. (2015) Principles of Copula Theory. Boca Raton: Chapman and Hall/CRC.CrossRefGoogle Scholar
Frahm, G., Junker, M. and Schmidt, R. (2005) Estimating the tail-dependence coefficient: Properties and pitfalls. Insurance: Mathematics and Economics, 37, 80–100.Google Scholar
Furman, E., Kuznetsov, A., Su, J. and Zitikis, R. (2016) Tail dependence of the Gaussian copula revisited. Insurance: Mathematics and Economics, 69, 97–103.Google Scholar
Furman, E., Su, J. and Zitikis, R. (2015) Paths and indices of maximal tail dependence. ASTIN Bulletin: The Journal of the International Actuarial Association, 45, 661–678.CrossRefGoogle Scholar
Hua, L. and Joe, H. (2011) Tail order and intermediate tail dependence of multivariate copulas. Journal of Multivariate Analysis, 102, 1454–1471.CrossRefGoogle Scholar
Joe, H. (1993) Parametric families of multivariate distributions with given margins. Journal of Multivariate Analysis, 46, 262–282.CrossRefGoogle Scholar
Joe, H. (2014) Dependence Modeling with Copulas. Boca Raton: Chapman and Hall/CRC.CrossRefGoogle Scholar
Krupskii, P. and Joe, H. (2019) Nonparametric estimation of multivariate tail probabilities and tail dependence coefficients. Journal of Multivariate Analysis, 172, 147–161.CrossRefGoogle Scholar
Lai, T.L. (1974) Convergence rates in the strong law of large numbers for random variables taking values in Banach spaces. Bulletin of the Institute of Mathematics Academia Sinica, 2, 67–85.Google Scholar
Mason, D.M. (1982) Some characterizations of almost sure bounds for weighted multidimensional empirical distributions and a Glivenko-Cantelli theorem for sample quantiles. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 59, 505–513.CrossRefGoogle Scholar
McNeil, A.J., Frey, R. and Embrechts, P. (2015) Quantitative Risk Management: Concepts, Techniques and Tools (Revised Edition). Princeton: Princeton University Press.Google Scholar
Nelsen, R.B., Quesada-Molina, J.J., Rodríguez-Lallena, J.A. and Úbeda-Flores, M. (2001) Distribution functions of copulas: A class of bivariate probability integral transforms. Statistics and Probability Letters, 54, 277–282.CrossRefGoogle Scholar
Nelsen, R.B., Quesada-Molina, J.J., Rodríguez-Lallena, J.A. and Úbeda-Flores, M. (2003) Kendall distribution functions. Statistics and Probability Letters, 65, 263–268.CrossRefGoogle Scholar
Nelsen, R.B. (2006) An Introduction to Copulas, 2nd edition. New York: Springer.Google Scholar
Su, J. and Furman, E. (2017) Multiple risk factor dependence structures: Copulas and related properties. Insurance: Mathematics and Economics, 74, 109–121.Google Scholar
Vovk, V. and Wang, R. (2020) Combining p-values via averaging. Biometrika (to appear).CrossRefGoogle Scholar
Wang, R. and Zitikis, R. (2020) An axiomatic foundation for the Expected Shortfall. Management Science (to appear).CrossRefGoogle Scholar