  Data-driven methods that detect anomalies in times series data are ubiquitous
in practice, but they are in general unable to provide helpful explanations for
the predictions they make. In this work we propose a model-agnostic algorithm
that generates counterfactual ensemble explanations for time series anomaly
detection models. Our method generates a set of diverse counterfactual
examples, i.e, multiple perturbed versions of the original time series that are
not considered anomalous by the detection model. Since the magnitude of the
perturbations is limited, these counterfactuals represent an ensemble of inputs
similar to the original time series that the model would deem normal. Our
algorithm is applicable to any differentiable anomaly detection model. We
investigate the value of our method on univariate and multivariate real-world
datasets and two deep-learning-based anomaly detection models, under several
explainability criteria previously proposed in other data domains such as
Validity, Plausibility, Closeness and Diversity. We show that our algorithm can
produce ensembles of counterfactual examples that satisfy these criteria and
thanks to a novel type of visualisation, can convey a richer interpretation of
a model's internal mechanism than existing methods. Moreover, we design a
sparse variant of our method to improve the interpretability of counterfactual
explanations for high-dimensional time series anomalies. In this setting, our
explanation is localised on only a few dimensions and can therefore be
communicated more efficiently to the model's user.
