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A copula-based correlation measure and its application in Chinese stock market. (English) Zbl 1186.91236

Summary: In this paper, a copula-based correlation measure is proposed to test the interdependence among stochastic variables in terms of copula functions. Based on a geometric analysis of copula functions, a new derivation method is introduced to derive the Gini correlation coefficient. Meantime theoretical analysis finds that the Gini correlation coefficient tends to overestimate the tail interdependence in the case of stochastic variables clustering at the tails. For this overestimation issue, a fully new correlation coefficient called Co is developed and extended to measure the tail interdependence. Empirical study shows that the new correlation coefficient Co can effectively solve the overestimation issue, which implies that the proposed new correlation coefficient is more suitable to describe the interdependence among stochastic variables than the Gini correlation coefficient.

MSC:

91G70 Statistical methods; risk measures
62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] DOI: 10.1142/S0219622007002721 · Zbl 1200.68223
[2] DOI: 10.1142/S0219622009003302 · Zbl 05560414
[3] Sklar A., Publication de 1’Institut de Statistique de 1’Universite de Paris 8 pp 229–
[4] DOI: 10.1080/01621459.1958.10501481
[5] Hollander M., Nonparametric Statistical Methods (1973) · Zbl 0277.62030
[6] Lehmann E. L., Nonparametrics: Statistical Methods Based on Ranks (1975) · Zbl 0354.62038
[7] DOI: 10.1214/aoms/1177699260 · Zbl 0146.40601
[8] DOI: 10.1214/aos/1176345528 · Zbl 0468.62012
[9] Genest C., American Statistician 40 pp 280–
[10] Daniels H. E., Journal of the Royal Statistical Society Series B 12 pp 171–
[11] Durbin J., Journal of the Royal Statistical Society Series B 13 pp 303–
[12] Hutchinson T. P., Continuous Bivariate Distributions, Emphasising Applications (1990) · Zbl 1170.62330
[13] Scarsini M., Stochastica 8 pp 201–
[14] DOI: 10.1201/b13150
[15] DOI: 10.1016/S0167-6687(02)00121-X · Zbl 1039.62043
[16] DOI: 10.1142/S0219622008002831 · Zbl 1153.91609
[17] Glover F., International Journal of Information Technology & Decision Making 7 pp 571–
[18] DOI: 10.1142/S0219622009003260 · Zbl 1175.91054
[19] Wei Y., Copula Theory and Its Application to Financial Analysis (2008)
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