Detecting bursts in data streams is an important and challenging task. Due to the complexity of this task, usually burst detection cannot be formulated using standard query operators. Therefore, we show how to integrate burst detection for stationary as well as non-stationary data into query formulation and processing, from the language level to the operator level. Afterwards, we present fundamentals of threshold-based burst detection. We focus on the applicability of time series forecasting techniques in order to dynamically identify suitable thresholds for stream data containing arbitrary trends and periods. The proposed approach is evaluated with respect to quality and performance on synthetic and real-world sensor data using a full-fledged DSMS.