Recently, due to the global competition companies active in different industries started to be concerned about the customer churn. With a churn rate of 30%, the telecommunications sector takes the first place on the list. The telecommunications operators need to identify customers who are at risk of churning by implementing predictive models. In this paper, we present an advanced data mining methodology which predicts customer churn in the pre-paid mobile telecommunications industry using a call details records dataset that consists of 3333 customers with 21 attributes each. We first apply the principal component analysis algorithm to reduce the dimensionality of the data and eliminate the problem of multicollinearity. To implement the predictive models, on the resulted principal components and discrete variables we initially propose and then apply three machine learning algorithms: neural networks, support vector machines, and Bayesian networks. To evaluate the models, we use the confusion matrix, the gain measure and the ROC curve.