Research On Shanghai Stock Index Forecast And Portfolio Investment Based On ARIMA And GARCH Model

In order to accurately predict the Shanghai stock index and study the optimal portfolio investment,this paper studies the Shanghai stock index,which can reflect the changes of the stock market.In the process of completion,it follows the method of combination of empirical and theoretical research.Starting from the research of th e development of things' own rules,and based on this,it briefly introduces the ARIMA and GARCH models Based on the data of A-share Shanghai index and four stocks with strong pertinence,the model is established and the feasibility of the model is tested.In this paper,we first fit the trend of the daily closing price of A-share Shanghai stock index in China,and test its auto correlation and partial correlation coefficient to find that it is non-stationary.Then we use the first-order logarithmic difference processing to find that it is stable,which is suitable for ARIMA model.In order to avoid the unreasonable parameters of the model,the ARIMA(2,1,2)model is compared with the AIC criterion through the auto correlation and partial correlation coefficients,and the conclusion that the ARIMA(2,1,2)model fits the data of Shanghai stock index is the best.Secondly,the parameters of ARIMA(2,1,2)model are fitted under the principle of maximum likelihood estimation.Based on this model,the closing price of China's A-share Shanghai stock index in the next five days is predicted,and the predicted value is compared with the real value outside the sample.The relative error of the predicted result is less than 2%,and the A-share Shanghai stock index in the next 20 trading days is given.Through comparison,we get the conclusion that the model fitted in this paper has better short-term prediction.Based on this,this paper selects the return rate of four stocks of Petro China,Sinopec,Bank of China and industrial and Commercial Bank of China,which account for a large proportion of the Shanghai stock index,to study the portfolio strategy.This paper uses GARCH model to solve the average return and risk loss rate of four stocks in the next 10 days,introduces optimistic coefficient to express the risk bearing capacity of shareholders,establishes an optimization model and obtains the optimal portfolio investment scheme under different optimistic coefficient,which has obvious practical significance.The empirical research of this paper shows that the first-order differential auto regressive moving average model and conditional heteroscedasticity model can achieve better results in the short-term prediction of Shanghai stock index and the optimization of investment portfolio,and can give some guidance to investors.