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 tai...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.展开更多
It has been argued that fitting a t-copula to financial data is superior to a normal copula. To overcome the shortcoming that a t-copula only has one parameter for the degrees of freedom, the t-copula with multiple pa...It has been argued that fitting a t-copula to financial data is superior to a normal copula. To overcome the shortcoming that a t-copula only has one parameter for the degrees of freedom, the t-copula with multiple parameters of degrees of freedom has been proposed in the literature, which generalizes both the t-copulas and the grouped t-copulas. Like the inference for a t-copula, a computationally efficient inference procedure is to first estimate the correlation matrix via Kendall's τ and then to estimate the parameters of degrees of freedom via pseudo maximum likelihood estimation. This paper proposes a jackknife empirical likelihood test for testing the equality of some parameters of degrees of freedom based on this two-step inference procedure, and shows that the Wilks theorem holds.展开更多
基金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)
文摘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.
基金supported by Simons Foundation and National Natural Science Foundation of China(Grant Nos.11571081 and 71531006)。
文摘It has been argued that fitting a t-copula to financial data is superior to a normal copula. To overcome the shortcoming that a t-copula only has one parameter for the degrees of freedom, the t-copula with multiple parameters of degrees of freedom has been proposed in the literature, which generalizes both the t-copulas and the grouped t-copulas. Like the inference for a t-copula, a computationally efficient inference procedure is to first estimate the correlation matrix via Kendall's τ and then to estimate the parameters of degrees of freedom via pseudo maximum likelihood estimation. This paper proposes a jackknife empirical likelihood test for testing the equality of some parameters of degrees of freedom based on this two-step inference procedure, and shows that the Wilks theorem holds.
