Early detection of network failures and performance degradations is a key to rapid fault recovery and robust networking, and has been receiving increasing attention lately. In this paper we present a fault diagnostic methodology, based on the characterization of the dynamic statistical properties of traffic normality in order to detect network anomalies. Anomaly detection is based on the concept that perturbations of normal behavior suggest the presence of faults. In order to design a system that provides an accurate identification of the normal network traffic behavior, we first develop an anomaly-tolerant non-stationary traffic prediction technique, which is capable of removing both single pulse and continuous anomalies. Furthermore we design and introduce dynamic thresholds, and based on them we define adaptive anomaly violation as a combined function of both magnitude and duration of the traffic deviations. Finally numerical results are presented that demonstrate the operational effectiveness and efficiency of the proposed approach.