The Construction And Application Of The Parameter Disturbance Copulas Family

Copula has a wider adaptability in portraying the correlation between random variables,because it can describe not only linear correlations but also nonlinear correlations.Copula with this advantage have been fully applied in complex and volatile financial,insurance and risk Management and other fields.Firstly,the application field of Copula theory is broadened,and some methods of fitting data for commonly used Copula are modified.It is applied in the field of meteorological research,and the correlation between temperature in Tianjin and Shanghai in the four quarters of 2017 is studied.The relevant structural model of temperature in cities throughout the year provides some reference and help for people's travel and economic exchanges between the two places.Furthermore,with the diversification of problems in different application fields,we need to construct Copula which is more flexible and applicable.This paper constructs a class of one-parameter perturbed Copulas by using perturbed construction method.The calculation formulas of four kinds of the dependence measures are given and proved.And for the one-parameter perturbation of copulas,the variation of the four kinds of tail correlation coefficients in the main diagonal part and the sub-diagonal part is studied.Furthermore,the variation law of Kendall's r and Spearman's ? with the perturbation parameter is studied.Finally,the method of generating random numbers by copula is used to carry out random simulation and verify the conclusion.Thirdly,based on the quadratic structure of copula,a new class of copulas is constructed by the two-parameter composite perturbations.It is proved that the two-parameter composite perturbations of copulas can be transformed into Plackett-Copulas under invariance conditions.The calculation formulas of four kinds of the dependence measures are proved and the changes of four kinds of tail correlation coefficients of the two-parameter composite perturbation of copulas in the main diagonal part and the sub-diagonal part are studied.Finally,in order to compare the effect of the newly constructed Copulas and the original Copula in application.Using the temperature data and taking the theoretical Copula and the empirical Copula as the difference and taking the square by squared Euclidean distance method,and the optimal model is obtained with the shortest distance.The newly constructed two perturbed Copulas not only broaden the range of dependence measures,but also increase the accuracy of fitting empirical data by adding the perturbation to the original Copula.In contrast,the two-parameter composite perturbation of Copulas has better superiority.