Prediction Of Shanghai Composite Index Based On PCA-GARCH-MIDAS-LSTM Model

The stock market is an important part of the national economy,and it is also the vanguard market of the national economic development.The change of the national economic development will cause the fluctuation of the stock market,and the change of the stock market will also affect the development speed of the national economy,and the two affect each other.The stock market is full of unpredictable changes,which are fundamentally influenced by many factors.Accurate prediction of the trend and range of the stock market can serve as a vane for investors to make investment decisions,and to a certain extent increase the return on investment and reduce investment risks.Macroeconomic indicators and volatility is one of the important factors affect stock movements,for the extracting volatility of macroeconomic indicators of selection and build the model of appeared a lot of research achievements,but there are two common problems,the traditional research on the one hand is the small number of variable selection methods to handle complex,on the other hand is can only handle with frequency according to the traditional model,based on the above consideration,This article selects the principal component analysis(PCA)and generalized autoregressive conditional heteroscedasticity mixed data sampling model(GARCH-MIDAS)build a portfolio model,the PCA model is mainly used for dimension of macroeconomic variables that this article can select multidimensional macroeconomic variables as the data source,on the one hand,as far as possible to ensure the integrity of the stock market information,On the other hand,it also makes up for the problem of multicollinearity between variables.Stock data have autocorrelation and conditional heteroscedasticity.GARCH model can effectively extract data volatility,but GARCH model can only deal with the same frequency data,while GARCH-MIDAS model can realize the fusion of low frequency data and high frequency data,and can analyze multidimensional data of different frequencies.The high frequency diurnal data are characterized by traditional GARCH model,and low frequency macroeconomic variables are characterized by MIDAS model.The combination of PCA model and GARCH-MIDAS model realizes the extraction of mixed frequency data volatility from high dimensional low frequency data and high frequency data.In front of the two models are belong to the traditional time series analysis model,it has limitations in dealing with nonlinear,containing noise data,and the length of time memory neural network model(LSTM)can make up for these deficiencies and have strong learning ability,can use the LSTM as a combination of the model framework,will influence factors as the input item input LSTM model.In this paper,the financial time series model and neural network model are combined,and the PCA-GARCH-MIDAS-LSTM model is constructed to explore the effective forecasting method of Shanghai Composite Index according to the macroeconomic factors.To be specific,firstly,PCA model is used to reduce the dimension of the high-dimension macroeconomic indicators,and the principal component factors containing the main information of the indicators are extracted.Then,GARCH-MIDAS model was used to extract the volatility of stock index based on principal component factors.Finally,the high frequency volatility and other selected daily data are input into the LSTM model to predict Shanghai Composite Index.In this paper,the daily closing price of Shanghai Composite Index,8 related daily data and the monthly data of 40 macro economic indicators in this time interval are selected,and the built model is used to forecast stock index.Meanwhile,the prediction effects of LSTM model,GARCHLSTM model and PCA-LSTM model are compared.The final prediction error and comparison figure show that the predicted value of the combined model constructed in this paper is closer to the real value,and the combination of single models achieves complementary advantages.