Fast, robust, and accurate anomaly detection for multivariate time series

Abstract Anomaly detection is a topic widely studied both in Statistics and Computer Science, with an ever growing literature in both disciplines. We present a novel, fast, robust, accurate, and widely applicable semi-supervised procedure for anomaly detection in multivariate time series, $${ FRA\! ^2\!Nk }{}$$ (Fast, Robust, and Accurate ANomaly detection). It comprises 5 steps: smoothing, multicollinearity mitigation, dissimilarity measurement, threshold selection, identification of the causes of the anomalies. $${ FRA\! ^2\!Nk }{}$$ can tackle issues from different challenging contexts, where signals can be highly multicollinear, have unknown distributions, and intertwine short-lived noise with longer-lived anomalies. Using several experiments, we demonstrate the generality, low computational cost, precision, and interpretability of $${ FRA\! ^2\!Nk }$$ . In particular: (i) Using public benchmark datasets from anomaly detection, we evaluate the computational cost and performance of $${ FRA\! ^2\!Nk }$$ against the semi-supervised methods from a recent literature review, finding that $${ FRA\! ^2\!Nk }$$ is effective, broadly applicable, and that it outperforms existing approaches in anomaly detection and runtime; (ii) Using such datasets we also show that $${ FRA\! ^2\!Nk }{}$$ can explain the causes of the discovered anomalies; (iii) Using simulation studies, we show that $${ FRA\! ^2\!Nk }{}$$ is robust to several possible issues in the data; (iv) Using a case study from an industrial partner, we show that $${ FRA\! ^2\!Nk }{}$$ is effective.