Detection of abnormal internet traffic has become a significant area of research in network security. Due to its importance, many predictive models are designed by utilizing machine learning algorithms. The models are well designed to show high performances in detecting abnormal internet traffic behaviors. However, they may not guarantee reliable detection performances for new incoming abnormal internet traffic because they are designed using raw features from imbalanced internet traffic data. Since internet traffic is non-stationary time-series data, it is difficult to identify abnormal internet traffic with the raw features. In this study, we propose a new approach to detecting abnormal internet traffic. Our approach begins with extracting hidden, but important, features by utilizing discrete wavelet transformation. Then, statistical analysis is performed to filter out irrelevant and less important features. Only statistically significant features are used to design a reliable predictive model with logistic regression. A comparative analysis is conducted to determine the importance of our approach by measuring accuracy, sensitivity, and the Area Under the receiver operating characteristic Curve. From the analysis, we found that our model detects abnormal internet traffic successfully with high accuracy.