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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.