Research On The Prediction Of The CSI 300 Index Based On Functional Partial Linear Model

With the improvement of the data collection system,all kinds of data can be completely retained.High-frequency data within a certain period will show functional characteristics,this type of data is called functional data.At present,the functional data analysis method has been applied to the fields of biology,climate,etc.The 5-minute high-frequency data of the stock price index has the characteristics of functional data and can also be regarded as a functional data.This thesis mainly uses the functional data model to predict the stock index,and uses the functional data analysis method to construct the stock index of the Xinjiang sector.This thesis first reviews the functional data models and functional data analysis methods used.This thesis mainly uses two types of functional data models,namely functional partial linear regression model(FPLRM)and functional time series model(FTSM).For the variable settings of the two models,the response variable of functional partial linear model is a scalar variable,and the predictor variable contains both scalar and functional variables.The response variable and predictor variable of functional time series model are both functional variables.Functional partial linear model is divided into semi-functional partial linear regression models(SFPLRM)and partial functional linear regression models(PFLRM)according to whether non-parametric methods are used for modeling.This thesis mainly uses three functional data models to predict the future dynamic curve of the stock index.The training data is selected from the 5-minute stock index data of the CSI 300 Index for a total of 41 days from April 17 to June17,2020.The response variable of functional partial linear model is a scalar,so it can't predict the future stock index dynamic curve.To overcome this problem,this thesis established a total of 48 models for the stock index data at 48 time points in a day.The 4)-th(4)=1,...,48)model uses the stock index data of the 4)-th time point on the 2nd?41th day as the response variable of the model,and the scaler variables and stock index data functional variables from 1 to 40 days are used as predictors.The forecast results of the model are arranged in chronological order,and the function curve is restored by interpolation method,the function curve is the stock index dynamic prediction curve.By comparing the prediction results,semi-functional partial linear regression model has the smallest mean square error,and partial functional linear regression model has the second smallest mean square error.Therefore,the prediction effect of semi-functional partial linear regression model is the best,the functional time series model is the worst.Through the comparison of the timeconsuming of the three models,the semi-functional partial linear regression model has the longest time-consuming,approximately eight times that of partial functional linear regression models.Finally,this thesis uses the daily closing price data of 57 stocks in the Xinjiang to construct a fourier basis function model,insert a smoothing term,and use generalized cross-validation(GCV)to select appropriate smoothing parameters,and process the original data into a better fitting effect.Through functional principal component analysis,eight stocks with the highest first principal component scores are selected as the most representative stocks in the Xinjiang.This thesis uses the daily 5-minute data of selected stocks to construct a daily stock index curve.Predicting one day in the future through semi-functional partial linear regression model,the prediction curve and the real curve trend are the same,indicating that the prediction effect of the model is good.