Online social networks are actively involved in the removal of malicious social bots due to their role in the spread of low quality information. However, most of the existing bot detectors are supervised classifiers incapable of capturing the evolving behavior of sophisticated bots. Here we propose MulBot, an unsupervised bot detector based on multivariate time series (MTS). For the first time, we exploit multidimensional temporal features extracted from user timelines. We manage the multidimensionality with an LSTM autoencoder, which projects the MTS in a suitable latent space. Then, we perform a clustering step on this encoded representation to identify dense groups of very similar users -- a known sign of automation. Finally, we perform a binary classification task achieving f1-score $= 0.99$, outperforming state-of-the-art methods (f1-score $\le 0.97$). Not only does MulBot achieve excellent results in the binary classification task, but we also demonstrate its strengths in a novel and practically-relevant task: detecting and separating different botnets. In this multi-class classification task we achieve f1-score $= 0.96$. We conclude by estimating the importance of the different features used in our model and by evaluating MulBot's capability to generalize to new unseen bots, thus proposing a solution to the generalization deficiencies of supervised bot detectors.