  The challenge of efficiently identifying anomalies in data sequences is an
important statistical problem that now arises in many applications. Whilst
there has been substantial work aimed at making statistical analyses robust to
outliers, or point anomalies, there has been much less work on detecting
anomalous segments, or collective anomalies, particularly in those settings
where point anomalies might also occur. In this article, we introduce
Collective And Point Anomalies (CAPA), a computationally efficient approach
that is suitable when collective anomalies are characterised by either a change
in mean, variance, or both, and distinguishes them from point anomalies.
Theoretical results establish the consistency of CAPA at detecting collective
anomalies and, as a by-product, the consistency of a popular penalised cost
based change in mean and variance detection method. Empirical results show that
CAPA has close to linear computational cost as well as being more accurate at
detecting and locating collective anomalies than other approaches. We
demonstrate the utility of CAPA through its ability to detect exoplanets from
light curve data from the Kepler telescope.
