Abstract: The paper uses an ARMAARCH model with three different types of noise to fit Shanghai and Shenzhen stock index return distribution. The result of the goodness of fit test with the stochastic simulation method shows that the ARMAARCH model with fractal Gaussian noise can characterize the volatility of Shanghai and Shenzhen stock returns, such as long dependence, fat tails and volatility clustering. Further, two different types of CopulaARMAARCH models are used to fit the dependence between Shanghai and Shenzhen stock indexes, and the result of the goodness of fit test with the stochastic simulation method shows that the CopulaARMAARCH model with fractal Gaussian noise can better characterize the VaR of volatility of Shanghai and Shenzhen stock returns.