Double Robust Sparse Regression Model And Its Application In Index Tracking

Passive investment strategy has attracted the attention of investors.As the most popular index tracking problem,it has also attracted the interest of scholars from all walks of life.According to the existing index tracking model,this paper explores deeply and tries to use a new model to track the index.At the same time,it considers the non short selling,transaction cost,variable selection and other constraints.The passive investment strategy needs to accurately copy the performance of the stock market index.At the same time,due to the limitation of transaction cost and the consideration of risk control,the index tracking model must have sparsity in highdimensional and non negative cases.As we all know,LASSO penalty has a good variable selection function,but when the sample size is fixed,with the increase of predicted variable dimensions,the generalization ability of LASSO regression begins to decline,mainly due to the over fitting phenomenon of the model.However,support vector regression,through the reference of ?-insensitive loss function,constructs a pipeline with a width of 2 ? on both sides of the fitting model.The error in the pipeline can be ignored,which can effectively reduce the over fitting of the model.In this paper,?-insensitive loss function and LASSO penalty are combined to construct sparse and robust support vector regression,which not only has the function of variable selection,but also can effectively reduce the over fitting of the model.In the part of numerical simulation and empirical analysis,we compare robust sparse support vector regression with LAD LASSO's return,and find that robust sparse support vector regression has relatively outstanding performance.In the empirical analysis,we select Shanghai Stock 50 in the first half of 2019 as the experimental data,from which we select 5,7,12 and 21 stocks to track the Shanghai Stock 50 index.With the increase of the number of stocks,robust sparse support vector regression shows excellent prediction ability,which shows that the model has certain availability and effectiveness in high latitude data analysis.