In this paper we modify the expectation maximization algorithm in order to estimate the parameters of the dynamic factor model on a dataset with an arbitrary pattern of missing data. We also extend the model to the case with a serially correlated idiosyncratic component. The framework allows us to handle efficiently and in an automatic manner sets of indicators characterized by different publication delays, frequencies and sample lengths. This can be relevant, for example, for young economies for which many indicators have been compiled only recently. We evaluate the methodology in a Monte Carlo experiment and we apply it to nowcasting of the euro area gross domestic product.