Studies of animal behavior are crucial to understanding animal-ecosystem interactions, but require substantial efforts in visual observation or sensor measurement. We investigated how classifying behavioral states of grazing livestock using global positioning data alone depends on the classification approach, the preselection of training data, and the number and type of movement metrics. Positions of grazing cows were collected at intervals of 20 seconds in six upland areas in Switzerland along with visual observations of animal behavior for comparison. A total of 87 linear and cumulative distance metrics and 15 turning angle metrics across multiple time steps were used to classify position data into the behavioral states of walking, grazing, and resting. Five random forest classification models, a linear discriminant analysis, a support vector machine, and a state-space model were evaluated. The most accurate classification of the observed behavioral states in an independent validation dataset was 83%, obtained using random forest with all available movement metrics. However, the state-specific accuracy was highly unequal (walking: 36%, grazing: 95%, resting: 58%). Random undersampling led to a prediction accuracy of 77%, with more balanced state-specific accuracies (walking: 68%, grazing: 82%, resting: 68%). The other evaluated machine-learning approaches had lower classification accuracies. The state-space model, based on distance to the preceding position and turning angle, produced a relatively low accuracy of 64%, slightly lower than a random forest model with the same predictor variables. Given the successful classification of behavioral states, our study promotes the more frequent use of global positioning data alone for animal behavior studies under the condition that data is collected at high frequency and complemented by context-specific behavioral observations. Machine-learning algorithms, notably random forest, were found very useful for classification and easy to implement. Moreover, the use of measures across multiple time steps is clearly necessary for a satisfactory classification.