Analysis Of The Dependency Between Stock Index Based On The Copula-ARIMA-GJR-GARCH Model

It is usually very difficult to figure out the dependencies when the return on assets distributes complicatedly. Especially when return on assets in the stock market isnon-normal, it’s nearly impossible to depict the joint distribution of returnon assetsaccurately. However, copula functions can resolve this problem. Copula functions is a statistical method which is used to describe the dependency structure of random variables. Jondeau and Rockinger(2006) proposed the Copula-GARCH model to estimate the joint distribution of return on asset. This paper draws on that, considering when we estimate theunivariate distributions, its volatility often exists leverage effect. SoARIMA-GJR-GARCH model, combining copula functions, is usedto yielda new method of estimatingthe joint distribution ofreturn on assets--the Copula-ARIMA-GJR-GARCH method. Practice proved that the method has an important effect on analyzing the dependency between returnon assets.The method first uses ARIMA-GJR-GARCH model to simulate the univariatedistribution, then simulates the joint distribution ofreturn on assets by combining copula functions. The copula functions include the Gaussian copula function and the Student-t copula function.Combiningthe empirical data in theChinese stock market, it estimates the joint distribution of the CSI 300 and the Shanghai composite index through the copula-ARIMA-GJR-GARCH model. The corresponding tests are also used to verify the rationality of the model. At the same time, by forecasting the future returns of two stock indices, It is founded that the model can capture the conditional dependency between the two stock indices very well.