基于变系数乘积模型的股指跟踪研究

Study on Stock Index Tracking Based on Variable Coefficient Product Model

随着经济的发展,股票投资进入大众视野,如何选择成分股对股票指数进行跟踪,越来越受到人们的关注,基于此,针对股票指数跟踪问题,提出了利用变系数乘积模型进行变量选择的一种方法。该方法基于B样条函数逼近技术,将LPRE准则和组SCAD惩罚函数结合起来,应用于变系数乘积模型,利用牛顿迭代法和局部二次近似给出了求解估计的实施步骤;为了验证所提方法的有效性,通过数值模拟,将变系数乘积模型SCAD惩罚方法(LPRE-S)与变系数模型最小二乘SCAD惩罚方法(LS-S)的结果进行了对比,为了验证所提方法的实用性,将LPRE-S估计方法与LS-S估计方法应用于深证红利指数,对其股指跟踪预测效果进行了比较;结果表明:LPRE-S估计方法选出真实模型的比率几乎接近1,能更好地达到变量选择的目的,且在股指跟踪中具有较好的预测效果。

With the development of economy,stock investment has come into public view.How to choose constituent stocks to track the stock index has been paid more and more attention by the people.Based on this,aiming at the problem of stock index tracking,a method of variable coefficient product model for variable selection is proposed.Based on B-spline function approximation technique,this method combines LPRE(Least Product Relative Error)criterion and group SCAD(Class Clipped Absolute Devation)penalty function to apply to the variable coefficient product model.The implementation steps of solving the estimation are given by Newton iterative algorithm and local quadratic approximation.In order to verify the effectiveness of the proposed method,the results of SCAD penalty method with variable coefficient product model(LPRE-S)and the least square SCAD penalty method with variable coefficient model(LS-S)were compared by numerical simulation.In order to verify the practicability of the proposed method,LPRE-S estimation method and LS-S estimation method are compared for the tracking and forecasting effect of dividend index in Shenzhen Stock Exchange.The results show that the ratio of the LPRE-S estimation on the method to select the real model is almost close to 1,which can better achieve the purpose of variable selection and has a good prediction effect in the stock index tracking.