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An extensible statistical framework for detecting anomalous time seriesincluding those with heavy-tailed distributions and non-stationarity inhigher-order moments is introduced based on penalized likelihood distributionalregression. Specifically, generalized additive models for location, scale, andshape are used to infer sample path representations defined by a parametricdistribution with parameters comprised of basis functions. Akaike weights arethen applied to each model and time series, yielding a probability measure thatcan be effectively used to classify and rank anomalous time series. Amathematical exposition is also given to justify the proposed Akaike weightscoring under a suitable model embedding as a way to asymptotically identifyanomalous time series. Studies evaluating the methodology on both multiplesimulations and real-world datasets also confirm that high accuracy can beobtained detecting many different and complex types of shape anomalies. Bothcode implementing GAWS for running on a local machine and the datasetsreferenced in this paper are available online.

Detecting Anomalous Time Series by GAMLSS-Akaike-Weights-Scoring