Variable Selection Methods In Cox Model And The Empirical Research On Stock Market

In recent years,the survival analysis methods and technologies are widely used in epidemiology and clinical medicine.The researchers has introduced them into the population statistics,actuarial science,economics and other fields gradually.But we find there are not too much applications in the financial fields.In this paper,the Cox proportional hazards regression model is used to study the stock transaction data.We use the basic constituent stocks of the CSI 300 as samples to find out the important factors which affect the stock's survival time.In order to find a more appropriate way to study the stock market,we compares the advantages and disadvantages of the variable selection methods in the case of Cox model.Firstly,we make numerical simulations when covariates are independent or correlative,resepectively,to compare the effect of variable selection between Lasso method and Elastic Net method in the case of Cox model.And the group effect of Elastic Net method is verified.These work make a preparation for the empirical analysis of the stock data of the basic constituent stocks of the CSI 300.Based on the Guotai Junan database,we collect 30 financial indicators of each share and take the first quarter of 2016 as the observation time.We define CSI 300 stock's survival peried to get the survival time and survival status of each stock in the quarter,and sort out the basic stock data needed.By analyzing the first quarter data of 2016,the correlation coefficients of 30 financial indexes are obtained.The descriptive statistical analysis of covariates is carried out to understand the basic characteristics of covariates.Then,we make the empirical analyses using the methods of Cox stepwise regression,Lasso and Elastic Net.The coordinate descent algorithm and the 10-fold cross-validation method are used to find the appropriate parameter values.Thus,we find the important covariates which affect the stock's life and analyze the degree and direction of their influences.Finally,we compare these three methods and summarize the common important covariates.It turns out that Lasso method and Elastic Net method are better than Cox stepwise regression method.The covariates selected by Lasso and Elastic Net methods are more efficient and simple than those selected by Cox stepwise regression method.There exists the multiple collinearity in the variables selected by Cox stepwise regression method,while it is not true in the case of Lasso method.The Elastic Net method has a significant group effect,that is to say,the covariates can be selected into the model,but Lasso method has not such property which can only select one into the model among these related variables.The Elastic Net method is superior to Lasso method,especially in the case of high dimension,small sample and strong correlation.In terms of fitting effect,Lasso method and Elastic Net method are superior to Cox stepwise regression method,and Lasso method has the best model fitting effect.