Collective anomaly detection in High-dimensional VAR Models

Hyeyoung Maeng; Idris Eckley; Paul Fearnhead

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arXiv · 2105.07538

Collective anomaly detection in High-dimensional VAR Models

Hyeyoung Maeng·Idris Eckley·Paul Fearnhead

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Abstract

There is increasing interest in detecting collective anomalies: potentially short periods of time where the features of data change before reverting back to normal behaviour. We propose a new method for detecting a collective anomaly in VAR models. Our focus is on situations where the change in the VAR coefficient matrix at an anomaly is sparse, i.e. a small number of entries of the VAR coefficient matrix change. To tackle this problem, we propose a test statistic for a local segment that is built on the lasso estimator of the change in model parameters. This enables us to detect a sparse change more efficiently and our lasso-based approach becomes especially advantageous when the anomalous interval is short. We show that the new procedure controls Type 1 error and has asymptotic power tending to one. The practicality of our approach is demonstrated through simulations and two data examples, involving New York taxi trip data and EEG data.

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Hyeyoung Maeng, Idris Eckley, Paul Fearnhead. 2021-05-16. Collective anomaly detection in High-dimensional VAR Models. https://arxiv.org/abs/2105.07538

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