Dynamic bivariate normal copula  

作　　者：LIAO Xin PENG Liang PENG ZuoXiang ZHENG YanTing 

机构地区：[1]School of Mathematics and Statistics, Southwest University [2]Department of Risk Management and Insurance, Georgia State University [3]Department of Finance, Beijing Technology and Business University

出　　处：《Science China Mathematics》2016年第5期955-976,共22页中国科学：数学（英文版）

基　　金：supported by the Simons Foundation;National Natural Science Foundation of China(Grant No.11171275);the Natural Science Foundation Project of CQ(Grant No.cstc2012jj A00029)

摘　　要：Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss（1989） showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss（1989）. A simulation study and real data analysis are presented too.

关 键 词：estimation normal copula tail dependence/independence 

分 类 号：O212.1[理学—概率论与数理统计]