Research On The Tracking Of The Entrepreneurship 300 Index Based On Two-step Dimensionality Reductio

Index tracking is an effective portfolio strategy in index fund management.How to sparse constituents and optimize the weights of stocks have become a hot spot in the research fields of securities and funds.In order to optimize the weights of stocks and reduce transaction costs,this paper studies the ultra-high dimensional index tracking methods which includes the following several aspects.Firstly,a two-step dimensionality reduction method is proposed by combining fea-ture screening and non-negative regression methods.Step 1,the feature screening method is used for a large-scale dimensionality reduction of constituent stocks.Then,an iterative Hoeffding’s D Sure Independence Screening（HD-ISIS）method is proposed for ultra-high dimensionality reduction.Step 2,non-negative regression methods are employed to re-duce the stocks’dimensions and estimate the coefficients simultaneously.In addition,a new restricted least absolute deviation（LAD）method called NNFLAD（Non-Negative and Full-investment constraints of Least Absolute Deviation）is considered.Secondly,by combining Sure Independence Screening（SIS）,Iterative SIS（ISIS）,Ho-effding’s D SIS（HD-SIS）,HD-ISIS,Non-Negative Least Squares（NNLS）,Non-Negative LAD（NNLAD）and NNFLAD methods,six methods of two-step dimensionality reduc-tion are considered in entrepreneurial 300 index tracking.Lastly,the empirical analysis shows that these six two-step dimensionality reduction methods’portfolios have the lowest transaction cost in(9₉)=[9)/7)2)（9）)];two-step dimen-sionality reduction methods based on iterative screening perform better than those of without iterating;the robust two-step dimensionality reduction methods’performances are not outstanding because there are fewer outliers in entrepreneurial 300 index’s dai-ly rate of return data,instead ISIS+NNLS method has the best tracking performance among these six methods.However,in a certain range of allowable tracking error,HD-ISIS+NNFLAD method conforms to the actual needs of index tracking problems better and also has significant application value.