Learning compressed representations of multivariate time series (MTS) facilitates data analysis in the presence of noise and redundant information, and for a large number of variates and time steps. However, classical dimensionality reduction approaches are designed for vectorial data and cannot deal explicitly with missing values. In this work, we propose a novel autoencoder architecture based on recurrent neural networks to generate compressed representations of MTS. The proposed model can process inputs characterized by variable lengths and it is specifically designed to handle missing data. Our autoencoder learns fixed-length vectorial representations, whose pairwise similarities are aligned to a kernel function that operates in input space and that handles missing values. This allows to learn good representations, even in the presence of a significant amount of missing data. To show the effectiveness of the proposed approach, we evaluate the quality of the learned representations in several classification tasks, including those involving medical data, and we compare to other methods for dimensionality reduction. Successively, we design two frameworks based on the proposed architecture: one for imputing missing data and another for one-class classification. Finally, we analyze under what circumstances an autoencoder with recurrent layers can learn better compressed representations of MTS than feed-forward architectures.