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

An extensible statistical framework for detecting anomalous time series including those with heavy-tailed distributions and nonstationarity in higher-order moments is introduced based on penalized likelihood distributional regression. Specifically, generalized additive models for location, scale, and shape are used to infer sample path representations defined by a parametric distribution with parameters comprised of basis functions. Akaike weights are then applied to each model and time series, yielding a probability measure that can be effectively used to classify and rank anomalous time series. A mathematical exposition is also given to justify the proposed Akaike weight scoring under a suitable model embedding as a way to asymptotically identify anomalous time series. Studies evaluating the methodology on both multiple simulations and a real-world dataset also confirm that anomalies can be detected with high accuracy. Both code implementing the algorithm for running on a local machine and the datasets referenced in this article are available online.