基于邻近梯度算法求解Lasso回归模型在证券指数的应用研究

Research on the Application of Lasso Regression Model Based on Proximity Gradient Algorithm in Stock Index

摘要: 在证券市场中，指数跟踪是投资者进行资产配置和风险管理的重要手段。传统的指数跟踪方法往往有模型解释性差、计算复杂度高等问题。因此，探索新的算法和技术以提升指数跟踪的效果具有重要意义。本文考虑Lasso回归模型来进行变量选择，首先介绍了Lasso回归模型基本原理，然后利用邻近梯度算法求解回归系数，该解具有稀疏性，旨在众多的变量中精确选择有效的部分变量来预测证券指数。最后利用沪深300指数以及其成分股的收盘价格作为分析数据，得出小部分股票就可以达到几乎相同的拟合效果，通过实例说明该方法在证券指数跟踪中有一定的有效性和优越性，能够实现更稀疏的变量组合，给证券指数跟踪提供了新的思路和方法。

Abstract: In the security market, index tracking is an important means for investors to allocate assets and manage risks. Traditional exponential tracking methods often have the problems of poor model interpretation and high computational complexity. Therefore, it is of great significance to explore new algorithms and techniques to improve the effect of exponential tracking. In this paper, Lasso regression model is considered for variable selection. Firstly, the basic principle of Lasso regression model is introduced, and then the adjacent gradient algorithm is used to solve the regression coefficient. The solution is sparse, aiming at accurately selecting effective part of the variables to predict the stock index from many variables. Finally, using the closing prices of CSI 300 index and its component stocks as analysis data, a small number of stocks can achieve almost the same fitting effect. An example shows that the method has certain effectiveness and superiority in securities index tracking, and can realize sparser variable combination, which provides a new idea and method for securities index tracking.