Abstract: There is increasing interest in detecting collective anomalies: potentially short periods during which the features of data change, before reverting back to normal behavior. We propose a new method for detecting a collective anomaly in the vector autoregressive (VAR) models. We focus on situations in which the change in the VAR coefficient matrix at an anomaly is sparse, that is, 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 the 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 the type-I error and has asymptotic power tending to one. The practicality of our approach is demonstrated using simulations and two data examples, involving New York taxi trip data and EEG data, respectively.

Key words and phrases: Collective anomaly, epidemic change, high-dimensional time series, Lasso, sparse changes, vector autoregressive model.