In non-destructive testing, acoustic emission testing is an established technique with numerous applications in academia and industry. In nearly all applications, the detection of relevant acoustic emission signals in continuous structure-borne sound recordings is a crucial step that forms the basis for subsequent analyses and should therefore neither miss any relevant acoustic emissions nor detect too many irrelevant events. That is because, in its most prevalent form, acoustic emission testing utilizes ultrasound signals that require large amount of storage, which might be an economically limiting factor especially for structural health monitoring of large civil infrastructures. In these monitoring applications, the signal-to-noise ratio is also expected to be worse compared to more controlled laboratory conditions, as they can be often found, for example, in materials research. We therefore propose the use of linear prediction, a time series forecasting technique, to extract relevant acoustic emissions from continuous recordings. The proposed methodology utilizes the residual between the signal predicted from a linear combination of previous time steps and the actual measurement to detect any anomalous events. Since the linear predictor can be initialized using the environmental noise only, no specific knowledge of the acoustic emission signals of interest is required beforehand and hence can automatically adapt to each measurement environment. We compare our approach with a simple amplitude-based detection as it is commonly implemented in commercially available acoustic emission systems. Especially for low signal-to-noise ratios, an increase in the area under the receiver operating characteristic curve of up to 0.6 compared to the amplitude-based detection is found.