Purpose: Predicting the movement of stock prices is a very challenging task because the characteristics of the stock market are complex, non-linear, and full of uncertainty. Many approaches have been applied for predicting the movement of stock prices ranging from simple linear statistical approaches such as discriminant analysis (DA) to complex machine learning approaches such as support vector machines (SVM). Both DA and SVM are approaches that can be used to do classifications such as separating stock price trends into several classes. By designing a number of prediction models that also apply the feature selection process, the level of prediction accuracy and the factors that can influence both approaches can be compared and analysed. Methodology: In this study, the trends of stock price movements are classified into two classes, namely "highly possible to go up" and "highly possible to go down or be neutral" in which the class separation is based on technical, fundamental, financial, and beta coefficient data from issuers on the Indonesia Stock Exchange (IDX). By using this data, a number of prediction models with specific prediction periods were trained and then used to predict the trends of stock price movements on the IDX. The prediction periods used in this study are ranging from 1 month to 9 months. Findings: The results show that SVM outperforms DA in terms of classification accuracy. This study also implies that several factors such as the selection of features in the DA and SVM models and the selection of kernel functions and parameters in the SVM model affect the performance of the classification model designed. Originality/value: The stepwise linear regression (SLR) and sequential forward selection (SFS) methods are applied to select the features that are most relevant so that the performance of each prediction model increases. The SFS method in this study is based on the k-fold cross-validation and the results of the SVM training-testing process as the criterion test. This proposed criterion test aims to increase the effectiveness of the feature selection process in the SFS method. The application of Bayesian optimization is proposed to optimize the parameters in the SVM model training process. This Bayesian optimization has proven to be far better than other parameter optimization approaches.