Prediction Of Stock Price With Mixed Data Based On Full Functional Linear Model

In today's big data era,people can easily obtain high-frequency data.In the financial field,the data collected is more frequently updated than the previous data.These data are similar to continuous functions,but also have the corresponding characteristics of functions.Based on these reasons,functional data analysis method can be considered when building models with high-frequency financial data.Functional data analysis is a kind of method that arises at the historic moment with the change of data form.The relationship between the response variables and the prediction variables of the full functional linear model can be regarded as a random process in an independent space,so that the density of the sample data can be inconsistent.Using the property of the full functional linear model,we can make full use of the mixed data to establish the regression model in the process of establishing the model,and predict the stock price fluctuation.Firstly,the functional data analysis methods are sorted out in detail,including the common functional data smoothing method,principal component analysis method and the general definition of full functional linear model.Secondly,the current two common methods for full functional linear model modeling are compared.In the simulation study,the mixed data is simulated by adjusting the number of observation points of single sample of response variable and prediction variable,that is,each sample curve of response variable has 50 observation points,each sample curve of prediction variable has 200 observation points,and the training set has 100 sample curves,There are 500 curves in the test set.Through this method,simulation study is set up to compare the feasibility of signal compression method and PACE-reg method(Functional linear regression via principal component analysis through conditional expectation)in the modeling of mixed data and the comparison of fitting and prediction effects.The results show that mixed data can be generated by setting the number of observed values of response variables and prediction variables,The mean square prediction error(MSPE)and mean square estimation error(MSEE)are smaller,which means that the prediction effect of signal compression method is better in many cases.Finally,in the part of empirical analysis,we use the data of stock price and trading volume of 8 stocks from January 4 to January 22,2021 to establish the full functional linear model with signal compression method,and then use the data of the next 5 working days to test the set to get the predicted value,The results show that the mean square prediction error of them is small,and the prediction effect is good,which can better predict the fluctuation of stock price,Second,based on the weighted combination forecasting model,the forecasting results of the two methods are weighted to get the final result.