Abstract
It is an important puzzle in the financial market to predict stock return movement direction. In this chapter, we not only propose (group) penalized logistic regression with multiple indicators to predict up- or downtrends, but also propose group penalized trinomial logit regression with multiple indicator groups to predict stock return movement direction: uptrends, sideways trends and downtrends. For the former, we construct the corresponding coordinate descent (CD) algorithm to complete variable selection and obtain parameter estimator, and introduce two-class confusion matrix, Receiver Operating Characteristic (ROC) and the area under a ROC curve (AUC) to assess two-class prediction performance. For the latter, we develop a rapidly convergent group coordinate descent (GCD) algorithm to simultaneously complete group selection and group estimation, introduce the relatively optimal Bayes classifiers to identify class indexes, and finally adopt three-class confusion matrix, Kappa, PDI, ROC surface and hypervolume under the ROC manifold (HUM) to assess three-class prediction performance.