  This article proposes novel rules for false discovery rate control (FDRC)
geared towards online anomaly detection in time series. Online FDRC rules allow
to control the properties of a sequence of statistical tests. In the context of
anomaly detection, the null hypothesis is that an observation is normal and the
alternative is that it is anomalous. FDRC rules allow users to target a lower
bound on precision in unsupervised settings. The methods proposed in this
article overcome short-comings of previous FDRC rules in the context of anomaly
detection, in particular ensuring that power remains high even when the
alternative is exceedingly rare (typical in anomaly detection) and the test
statistics are serially dependent (typical in time series). We show the
soundness of these rules in both theory and experiments.
