Research On The Theory And Application Of Time-varying Copula Function

Copula is an important function to measure the correlation of random variables.It is widely used in the research of financial industry and economic market.As the internal and external environment of financial industry is changing dynamically,it is of great significance to introduce the time-varying Copula function to study the dynamic correlation between variables.This paper mainly studies the theory and application of time-varying Copula function.Firstly,from the perspective of Copula's nonparametric estimation method,proposing the time-varying Copula function based on kendall coefficient,and the time-varying Copula function was used to analyze the asymmetry and tail correlation between the output values of Chengdu and Deyang.Secondly,EWMA control chart is used to monitor the sensitivity of time-varying parameters of four Copula functions to sample drift.Based on the time-varying Copula function theory,the following research is done in this paper:Based on the nonparametric estimation method of Copula function,a kendall-dependent time-varying Copula function is proposed.The annual growth rate of output value in Chengdu and Deyang of sichuan province was selected as the research object,using static Copula and time-varying Copula to analyze the correlation between the industrial output value of Chengde and Deyang.Then,the tail correlation coefficient is selected to study the tail correlation between the industrial output value of the two regions,the results show that the time-varying Copula function is better than the static Copula,and there is a positive correlation and upper tail correlation between the industrial output value of Chengdu and Deyang.On the basis of EWMA control chart,the sensitivity of time-varying parameters of Copula function to sample drift was explored by monte carlo experiment and empirical analysis.Firstly,the time-varying parameters of Gumbel,Clayton,Frank and AMH Copula functions were calculated as the research object,using EWMA control chart to monitor the influence of sample mean and variance drift on time-varying parameters,that is to observe the change of the average running length of the Copula in the state of process out of control.Secondly,selecting the data of the Shanghai composite index and the hang seng index from2015 to 2019 as actual test samples,using EWMA control charts to monitor a specific drift in the sample.The empirical results are consistent with the monte carlo experiment results and both show that the time-varying parameters of Clayton function are the first to detect the sample changes when the sample has a small drift,indicating that the time-varying parameters of Clayton function are more sensitive to the small drift of sample mean and variance than other Copula functions.