关于参数型copula函数的拟合检验

在金融和保险中,copula函数是一种构造多元相关分布函数的有力工具．然而,怎样选择一个适当的copula函数用于拟合数据,并没有找到统一的方法．因此,基于copula函数的经验分布,我们提出了一种用于检验具有某种特定参数结构的copula函数拟合数据优良性的方法,并得到了此检验的渐近性质．由于该检验统计量的极限分布依赖未知参数,我们采用非参数蒙特卡罗方法确定临界值．我们做了一个简单的模拟来验证本文提出的检验方法的功效．

CHECKING THE ADEQUACY OF COPULAS WITH PARAMETRIC STRUCTURE

Copulas are powerful in modeling multivariate dependence distributions in finance and insurance. However, how to select a proper copula with a parametric structure to fit the available data is still in its infancy. To tackle this issue, we construct a goodness-of-fit test for checking the validity of copulas with some specific form. The asymptotic properties of our proposed test are established. Since the limiting distribution is not tractable, we herein introduce the Nonparametric Monte Carlo Test to determine the critical values. The empirical behavior is also investigated by simulations to evidence the efficiency of our test.