[1] Shi Aiju, Lin Jinguan,. Monotonicity of the tail dependence for multivariate t-copula [J]. Journal of Southeast University (English Edition), 2011, 27 (4): 466-470. [doi:10.3969/j.issn.1003-7985.2011.04.024]

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Monotonicity of the tail dependence for multivariate t-copula()

多元t-copula尾相依的单调性

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

27

Issue:

2011 4

Page:

466-470

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2011-12-31

Info

Title:

Monotonicity of the tail dependence for multivariate t-copula

多元t-copula尾相依的单调性

Author(s):

Shi Aiju¹;  2;  Lin Jinguan¹

¹Department of Mathematics, Southeast University, Nanjing 211189, China
²College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

石爱菊¹;  2;  林金官¹

¹东南大学数学系, 南京 211189; ²南京邮电大学理学院, 南京 210003

Keywords:

multivariate t-copula;  copula;  inverse gamma distribution;  monotonicity;  regularly varying function;  correlation coefficient

多元t-copula;  copula;  逆伽玛分布;  单调性;  正则变化函数;  相关系数

PACS:

O212.4

DOI:

10.3969/j.issn.1003-7985.2011.04.024

Abstract:

This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.

考虑了多元t-copula的上尾象限相依指数和上尾极值相依指数, 该t-copula是在相依结构下定义的.由于多元连续型随机变量的copula函数关于严格单调递增变换具有不变性质, 由此推导了多元t-copula的尾相依指数的精确表达式, 得到的结果明显比以往文献给出的结论更加简洁.然后, 讨论了这2个相依指数关于相关系数的局部单调性质:上尾极值相依指数关于相关系数是严格单调递增的, 但上尾象限相依指数的单调性比较复杂.通过蒙特卡罗模拟数据验证了结果的正确性.同时, 发现所有结论可以推广到生成随机变量是正则变化的分布类中.

References:

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Memo

Memo:

Biographies: Shi Aiju(1971—), female, graduate, associate professor; Lin Jinguan(corresponding author), male, doctor, professor, jglin@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No. 11001052, 11171065), the National Science Foundation of Jiangsu Province(No.BK2011058), the Science Foundation of Nanjing University of Posts and Telecommunications(No.JG00710JX57).
Citation: Shi Aiju, Lin Jinguan. Monotonicity of the tail dependence for multivariate t-copula[J].Journal of Southeast University(English Edition), 2011, 27(4):466-470.[doi:10.3969/j.issn.1003-7985.2011.04.024]

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