Predicting up and down trends for stock prices is an important puzzle in the financial field. Hu & Jiang (2021) proposed logistic regression with 6 technical indicators to predict up and down trends for Google's stock prices. In this paper we further propose the five penalized logistic regressions with 19 technical indicators: ridge (L2), lasso (L1), elastic net(EN), smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) to improve the prediction accuracy. Firstly, we combine the iterative weighted least square algorithm with the coordinate descent algorithm, and apply a training set to obtain parameter estimators and probability estimators. Then we adopt a test set to construct confusion matrices and receiver operating characteristic (ROC) curves, and apply them to assess their prediction performances. Finally we compare the proposed five prediction methods with logistic regression, support vector machine (SVM) and artificial neural network (ANN) , and found that the MCP penalized logistic regression performs the best. Therefore, we develop a new efficient prediction method to predict up and down trends for stock prices.