  In recent years, specific evaluation metrics for time series anomaly
detection algorithms have been developed to handle the limitations of the
classical precision and recall. However, such metrics are heuristically built
as an aggregate of multiple desirable aspects, introduce parameters and wipe
out the interpretability of the output. In this article, we first highlight the
limitations of the classical precision/recall, as well as the main issues of
the recent event-based metrics -- for instance, we show that an adversary
algorithm can reach high precision and recall on almost any dataset under weak
assumption. To cope with the above problems, we propose a theoretically
grounded, robust, parameter-free and interpretable extension to
precision/recall metrics, based on the concept of ``affiliation'' between the
ground truth and the prediction sets. Our metrics leverage measures of duration
between ground truth and predictions, and have thus an intuitive
interpretation. By further comparison against random sampling, we obtain a
normalized precision/recall, quantifying how much a given set of results is
better than a random baseline prediction. By construction, our approach keeps
the evaluation local regarding ground truth events, enabling fine-grained
visualization and interpretation of algorithmic results. We compare our
proposal against various public time series anomaly detection datasets,
algorithms and metrics. We further derive theoretical properties of the
affiliation metrics that give explicit expectations about their behavior and
ensure robustness against adversary strategies.
