  In recent years, there has been a growing interest in identifying anomalous
structure within multivariate data streams. We consider the problem of
detecting collective anomalies, corresponding to intervals where one or more of
the data streams behaves anomalously. We first develop a test for a single
collective anomaly that has power to simultaneously detect anomalies that are
either rare, that is affecting few data streams, or common. We then show how to
detect multiple anomalies in a way that is computationally efficient but avoids
the approximations inherent in binary segmentation-like approaches. This
approach, which we call MVCAPA, is shown to consistently estimate the number
and location of the collective anomalies, a property that has not previously
been shown for competing methods. MVCAPA can be made robust to point anomalies
and can allow for the anomalies to be imperfectly aligned. We show the
practical usefulness of allowing for imperfect alignments through a resulting
increase in power to detect regions of copy number variation.
