[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()

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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

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

Keywords:

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

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.

References:

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[11] Chan Y, Li H J. Tail dependence for multivariate t-copulas and its monotonicity[J]. Insurance: Mathematics and Economics, 2008, 42(2):763-770.
[12] Schmidt R. Tail dependence for elliptically contoured distributions[J]. Mathematical Methods of Operations Research, 2002, 55(2): 301-327.
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[14] Tong Y L. Probability inequalities in multivariate distributions [M]. New York: Academic Press, 1980: 131-179.

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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