Abstract:

Aiming at the complexity between the characteristics of high-dimensional datasets. This paper proposes replace L1 penalty in LR-Elastic Net with SCAD（Smoothly Clipped Absolute Deviation） penalty and MCP（Minimax Concave Penalty）, constructs LR-SCAD and LR-MCP models respectively, and uses ADMM（Alternating Direction Method of Multipliers）algorithm to solve. Simulation experiments show that LR-Elastic Net model is good at handling small sample data with correlation features, while LR-SCAD and LR-MCP models perform well in large sample data with correlation features. At the same time, the paper establishes LR-Elastic Net, LR-SCAD and LR-MCP strategies, and applies them to the data of the CSI 300 Index. Back-test results show that LR-SCAD and LR-MCP strategies perform better than LR-Elastic Net strategies in highly correlated data.

Key words: Elastic Net, Smoothly Clipped Absolute Deviation（SCAD）, Minimax Concave Penalty（MCP）, Alternating Direction Method of Multipliers（ADMM） algorithm, logistic regression, multi-factor stock selection

摘要：

针对高维度数据集特征之间的复杂性，而传统的L1惩罚项不满足Oracle性质的无偏性，将逻辑回归弹性网（LR-Elastic Net）中的L1惩罚项替换为SCAD（Smoothly Clipped Absolute Deviation）和MCP（Minimax Concave Penalty）惩罚项，分别构建了LR-SCAD和LR-MCP模型，在保留稀疏性的同时满足了无偏性，并利用ADMM（Alternating Direction Method of Multipliers）算法进行求解。通过模拟实验发现，LR-Elastic Net模型能很好地处理特征存在相关性的小样本数据，而LR-SCAD和LR-MCP模型在特征存在相关性的大样本数据中表现较好；建立LR-Elastic Net、LR-SCAD和LR-MCP策略，并应用于沪深300指数成分股数据。回测结果显示，LR-SCAD和LR-MCP策略在股票相关性很强的数据中比LR-Elastic Net策略表现更好。

关键词: 弹性网（Elastic Net）, SCAD, MCP, ADMM算法, 逻辑回归, 多因子选股