  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.
