Group Penalized Multinomial Logit Models and Stock Return Direction Prediction

Multinomial logit model(MLM) has been proposed as the most frequently regression model for multi-category response. To deal with correlated data, in this paper we propose G-LASSO/G-SCAD/G-MCP penalized MLM to exert class discovery and class prediction for high-dimensional multi-category classification problems. Firstly, we develop a group coordinate descent(GCD) algorithm to simultaneously complete group selection and group estimation, and prove the convergence to the proposed GCD algorithm under mild conditions. Secondly, we apply the training set and group estimations to obtain class probability estimators, choose the Bayes classifier to identify class index information, and introduce the testing set and a few measures to assess multi-category prediction performance. Simulations show that the proposed methods outperform LASSO/SCAD/MCP penalized MLM, 3 deep learning methods and 3 machine learning methods in terms of Kappa, PDI(polytomous discrimination index), Optimal or Average Accuracy. Finally, we combine group penalized MLM with 58 technical indicators to predict up trends, sideways trends and down trends for stock returns, and show that the proposed methods outperform the other 9 methods in terms of Accuracy, PDI, Kappa and HUM. Therefore, the proposed method can not only accommodate the correlation information, but also improve multi-category prediction performance by shrinking group coefficients.