Stock Index Tracking Based On Two Classes Of Improved Liu Estimation And Their Application

Stock index tracking is a passive portfolio management strategy,which develop rapidly in our country recent years.The performance of many funds at home and abroad has shown that passive portfolio management strategy is an effective investment management method.How to effectively track stock indices to provide more reference for fund companies and investors is getting more and more attention.Considering that stock data has very serious multicollinearity and stock index formula is constructed using a linear method,linear biased estimation is an effective stock index tracking solution.Besides,LIU regression is a kind of linear biased estimation with good statistical properties.Based on the LIU estimation,two classes of improved LIU estimation are proposed.One is a class of three-parameter estimation that combines least squares estimation and ridge estimation,and the other is a class of new estimation based on iterative LIU estimation.Theoretically,the necessary and sufficient conditions for these two new classes of estimation to be better than the least squares estimation under loss function of MSEM are given.It also proves the admissibility of the new class of three-parameter estimation.In addition,the paper theoretically gives the necessary and sufficient conditions for all regression parameters of the new class of estimation based on iterative LIU regression are non-negative.And an empirical analysis was carried out using these two new classes of estimation.Based on CSI 300 Index and the 5-minute closing price of its constituent stocks from August 1,2017 to November 9,2017,the least squares model,positive regression model,ridge regression model,the classical LIU regression model and LASSO regression model are established respectively.The empirical results obtained from the above five regression models are compared with the empirical results of two classes of newly proposed estimation.Empirical results show that the extrapolation tracking effect of the class of three-parameter estimation is good.Because the sum of the residuals of the class of three-parameter estimation are better than the sum of the residuals of the least squares estimation and the ridge estimation under the same parameters.In addition,the new class of estimation based on iterative LIU regression can reduce the sum of squares of the residuals of the test set significantly compared with the least squares estimation,positive estimation,ridge estimation,LASSO estimation and classical Liu estimation.The tracking effect is obviously superior to the other five estimation,and the new class of estimation based on iterative LIU regression can make the model get all regression coefficients are not negative,which has important practical significance in practical applications.