Modern Economics & Management Forum

This paper selects the daily closing price data of the Shanghai Composite Index from January 1, 2016 to December 31, 2017, excluding holidays, and preprocesses the data. After taking the logarithm and converting it into the rate of return data, the first-order difference is performed to make it into a stable time series, and then the ARMA(p,q) model is constructed. Through parameter significance test, residual test and characteristic root test, according to the minimum principle of AIC, the optimal model is finally determined to be ARMA(2,5) of sparse coefficient, and the expression of the model is obtained. The GARCH(1,1) model is established for the residual of ARMA(2,5), and the model expression is obtained. In order to directly predict the return rate of the Shanghai Composite Index, the ARIMA(2,1,5) model of the sparse coefficient is constructed for the return rate of the Shanghai Composite Index, and the model expression is obtained. By predicting the Shanghai Composite Index return data on January 2, 2018, it is found that the prediction error of the model is small, and it can be used for subsequent predictions.