It is found that the GARCH (1,1) model has a good fitting effect on the time series by the statistical analysis of the logarithmic yield of the closing price of the Shanghai Composite Index. Therefore, this paper first uses the model GARCH (1,1) predicts the daily closing price of the Shanghai Composite Index, and then uses the Fourier series to correct the predicted residuals to obtain the final prediction sequence. By comparing the average relative error of the two methods, The relative mean error of the FGARCH (1, 1) model is small and has certain applicability.