基于弹性网降维的两步估计回归模型的上证50股票指数追踪研究

Shanghai 50 Stock Index Tracking Research Based on Elastic Net Dimensionality Reduction Two-Step Estimation Regression Model

摘要: 随着我国金融产业的飞速发展，股票投资成为大众最为青睐的一种理财方式。如何较为有效地对股票指数进行追踪对各投资机构以及众多散户来说至关重要。文章对上证50综合指数日收盘价数据建立基于弹性网降维的两步估计回归模型，第一步先采用绝对约束估计和弹性约束估计对原始变量进行降维，再根据误差分析结果，选择使得指数追踪误差更小的解释变量作为指数追踪的研究对象，第二步用最小二乘估计建立经验回归方程，再使用逐步回归剔除不显著变量，寻找部分股票构成的最优的追踪组合。实证结果表明：弹性网降维的两步估计回归模型能更有效地对股票价格进行预测，指数追踪效果最好。

Abstract: With the rapid development of China’s financial industry, stock investment has become the most popular way of financing. How to track the stock index more effectively is very important for each investment institution and many retail investors. This paper establishes a two-step estimation regression model based on elastic net dimensionality reduction for the daily closing price data of Shanghai Composite Index 50. In the first step, absolute constraint estimation and elastic constraint estimation are used to reduce the dimensionality of the original variables. Then, according to the error analysis results, explanatory variables with smaller index tracking errors are selected as the research objects of index tracking. The second step is to establish the empirical regression equation with the least square estimation, and then use stepwise regression to eliminate the insignificant variables to find the optimal tracking combination of some stocks. The empirical results show that the two-step regression model of elastic net dimensionality reduction can predict the stock price more effectively, and the index tracking is the best.