Research And Application Of Dependency Measure Based Copula Function

The dependence of multi-dimensional random variables is an important index in statistical analysis and is often used in different fields of statistical analysis such as in the field of finance,conditional probability in time series,etc.especially in the era of big data,the dependence between random variables has been paid more and more attention.The dependence theory is mainly studied from three aspects:probabilistic integral transformation,Copula function and fragile model.As one of the research methods of dependency theory,Copula function provides the theoretical basis for the gradually refined dependency mechanism.Based on Copula function,this paper studies the dependence between two-dimensional random variables.The main work is as follows.(1)Based on the relative distance from random point to independent point,the definition of microcosmic dependence function is proposed,and seven basic properties of microcosmic dependence function are proved.According to the transformation law of Copula under the monotonic transformation of random variables,the variation law of the microscopic dependence function under the monotonic transformation of random variables is deduced.According to the local integrability of the microscopic dependence function,the local dependence of any random variable is given.(2)The relation and difference between different dependency measures are discussed.The rank correlation coefficients of FGM Copula function family and Marshall-Olkin Copula function family were statistically simulated.The theoretical and simulated values of rank correlation coefficients of two copulas were compared respectively.The results showed that Kendall of the two Copula families was closer to the truth value than Spearman’s simulation value.The simulation results of FGM Copula function with parameter 1 and Marshall-Olkin Copula function with parameter 0.5 are closer to the truth value.(3)A Copula model was established based on the daily return rate of Shanghai Stock Index A and B from 2016-1-1 to 2020-3-31 by MATLAB.Through the model test,it is found that binary T-Copula with the parameter of,can better fit the observed data of several days’return rate of A and B stock indexes.