Prediction Method Based On Clusterwise Linear Regression And Its Application To Stock Market

Stock market forecasting is a challenging task.Due to various factors such as market economy,business operations,and political decision,stock market forecasting is complex,dynamic,and unstable.The theory and method of intelligent control and pattern recognition are studied.This paper proposed a novel prediction method based on clusterwise linear regression(CLR)and applied it to the closing price prediction of stock market.Numerical results show that the novel prediction algorithm is feasible and effective.Clusterwise linear regression aims at clustering the dataset according to different linear pattern and finding the regression function of each subset simultaneously.Clusterwise linear regression is an important method which combines two typical data mining problems: clustering and regression.General clustering problems cluster dataset based on similarity,while the clusterwise linear regession classify the dataset according to minimal regression error criterion.This paper discusses three solving algorithms for clusterwise linear regression,including sp?th algorithm,EM algorithm,and nonsmooth nonconvex optimization approach.Like linear regression,the main application of clusterwise linear regression is data prediction.However,because the clusterwise linear regression method divides the dataset into multiple linear regression classes,which leads to the linear regreesion class to which the input data to be predicted belongs is unknown.Which regression coefficients should be used at this time is unknown causes the major difficulty of prediction method based on clusterwise linear regression.To solve this problem,we proposed a clusterwise linear regression prediction algorithm that uses multiple classification models to assist the classification of the input data.Firstly,the multi-classification model is trained based on the results of clustering linear regression Secondly,determining the cluster to which the input data to be predicted belongs according to the multi-classification model.Finally,the linear regression coefficient corresponding to this cluster are uesd for prediction.We give the approach two new names——Softmax-CLR and Softmax-CLR-weight.In order to prove the effectiveness of the proposed prediction algorithm,we compared these two approaches with internal prediction methods based on CLR.Numerical results demonstrate that novel approaches are more accurate than the existing algorithm.Then,this paper also compared the novel algprithm with external widely used prediction algorithm.Multiple linear regression,ridge regression,and artifical nueral network are included.It is concluded that the novel approach obtains similar performance to artificial neural networks and better performance than the other proposed methods.In terms of implementation,the Softmax-CLR prediction algorithm is applied to daily closing price prediction of Shanghai composite index.The independent variables include opening price,closing price,high price,low price,trading volume and trading amount before the forecast date.Closing price of next day is regarded as output.Support vector machine and artificial neural network these two regression models have extraordinary behavior on stock market prediction and they are compared with the proposed method.The prediction value and corresponding evaluation indicator obtained by these three models are shown in the table and figure.Softmax-CLR has achieved an average accuracy of 99.0406%,which is superior to artificial neural network and competitive with support vector machine.Softmax-CLR also has better stability and fitting effect than other two methods.In the subsequent research work,we can apply the novel proposed algorithms to the prediction of other time series data.