Copula-based Tail Correlation Theory And Its Application

Copula function is an important tool to study the correlation between variables.It not only reflects the correlation between variables but also reflects the construction between variables.This paper first introduces Copula's theory,and then studies the tail correlation from the perspective of regular change index,The relationship between the regular change index of Copula generators and the tail correlation coefficient of Archimedes was established,Finally,the tails correlation between the main atmospheric pollutants and PM_2.5 concentration in Wuhan is analyzed,the paper is divided into six part:The first part is the introduction,which mainly introduces the background and meaning of the Copula function and tail correlation research as well as the present situation of the research at home and abroad.Then it introduces the work content and the framework of this article.The second part introduces the basic theory of Copula function,including the definition of Copula function,the most important Archimedean Copula in Copula family,the correlation theory,including Pearson linear correlation,Kendall rank correlation and tail correlation.The third part introduces Copula function selection and parameter estimation method.The fourth part studies the relationship between tail correlation coefficient and Archimedean Copula generators,and studies the tail correlation of Archimedean Copula by using the regular variation index of the generator,the relationship between the regular change index of the original element and the correlation coefficient of the tail of the new generator is obtained for the compound element compound,convex combination,product structure,three methods for generating generators of the new Archimedean Copula with some kind of tail correlation are proposed by using the regular variation index of the primitive generators.The fifth part analyzes the linear correlation and tail correlation between PM_2.5and concentration in Wuhan,the sharp increase of concentration will lead to the sharp increase of PM_2.5 concentration.Finally,some suggestions are put forward for the treatment of PM_2.5 in Wuhan.The sixth part summarizes the work done in this paper and puts forward some further questions to be studied.