The Application Research On The Correlation Analysis Of Stock Market In Copula Function

With the globalization of economy and internationalization of financialmarket, the financial market becomes more connected, and the correlationshipamong them becomes more complicated which represents a nonlinear,asymmetric and tail dependence. Therefore, those traditional analytical methodsthat based on linear correlation coefficients can not accurately reflect thedependence relation among financial markets anymore. In1959, Sklar firstsuggested Copula function theory which stated that Copula function couldperfectly depict the related information between random variables.Since then,domestic and overseas scholars have conducted great studies of Copula function,but most of them focused on the theoretical research, such as the choice of dualcopula functions, making parameter estimation and goodness-of-fit test for thedual copula function selected and so on, and for multivariate variables researchis rare. Whereas the financial system is a complex system, to most problems, wecannot only consider the relationship between two variables, but need to studythe correlation between multiple variables. However, the model built by theexisting multivariate variable research methods often makes assumption thatdoes not meet the real situation in dealing with practical problems, but bringsdeviation which will impact the judgment of actual relationship among variables.To solve the problem, this article introduces a new method--Pair Copula, whichcan not only accurately reflect the dependencies among random variables, butalso very easily establish the density function of joint distribution and greatlysimplify the process of parameters estimation.The focus of this article consists of three parts: first,it makes a comparisonbetween the Copula function and the method of traditional stock marketcorrelation analysis, though which we can get the advantages of the Copula:(1)Copula function can research the marginal distribution and joint distributionseparately.(2) With the random variable monotone increasing,the Copulafunction can make the correlation fixed between the variables.(3) Copulafunction can capture the tail dependence between the variables. Second,Copula function plays an important role in the application of correlation analysis ofbinary linear equation. With the pairwise correlation analysis among HSI index,N225index, STI index and SSEC index. We can reach the conclusion that theGaussian Copula function and t Copula function can describe the pairwisecorrelation structure function better, but when we refer to the tail dependence,Clayton Copula function and Gumbel Copula function is more suitable. Third,we use the method of the Pair Copula to solve problem about the multivariaterandom variables, making HSI index, N225index, STI index and SSEC indexthe object of research. With the empirical research on the relationship betweenthe four stock market,the C Vine, D Vine and the theory of tail dependencecan help to conclude the correlation between the stock markets in themultivariate case and obtain good results.