We propose two solutions to outlier detection in time series based on recurrent autoencoder ensembles. The solutions exploit autoencoders built using sparsely-connected recurrent neural networks (S-RNNs). Such networks make it possible to generate multiple autoencoders with different neural network connection structures. The two solutions are ensemble frameworks, specifically an independent framework and a shared framework, both of which combine multiple S-RNN based autoencoders to enable outlier detection.  This ensemble-based approach aims to reduce the effects of some autoencoders being overfitted to outliers, this way improving overall detection quality. Experiments with two large real-world time series data sets, including univariate and multivariate time series, offer insight into the design properties of the proposed frameworks and demonstrate that the resulting solutions are capable of outperforming both baselines and the state-of-the-art methods.