基于Copula函数的深证成指与深市基金指数相依性的实证分析

摘要

选取2013年-2016年4年间,深证成分指数与深市基金指数的收益率数据,利用Copula函数的相关理论,用不同类型的Copula函数描述这2个变量间的相依性关系.首先,对于t-Copula和正态Copula,通过比较经验数据和拟合函数的平方欧氏距离来判断其优劣.然后,运用解析法判断Archimedean族的3种函数描述变量间相依性关系的优劣.最后,再对上述2种方法的结果进行比较,选出最优的Copula函数形式来描述两者之间的相依性关系.用拟合得到的最优的Copula函数来描述分析深市成指和深市基金之间的尾部相依性关系.%This paper chooses the data of the rate of daily return in 2013-2016 of Shenzhen composite index and Shen zhen fund index as well as uses relative theories and different forms of Copula function to describe the dependent relationship between the two random variables.Firstly,whether t-Copula or normal Copula is good is decided by the comparison of the square Euclidean distances between the empirical data and the Copulas.Secondly,the goodness of fit to three of Archimedean Copulas is tested by analyticalmethod.Lastly,compare the two Copulas with the above-mentioned steps.In this way,the best fitted Copula is obtained.Then it is used to analyze the tail-dependence between the Shenzhen stork market and Shenzhen fund market.