Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical performances of matrix factorization for time series. In this paper, we extend the results known for matrix estimation in the i.i.d setting to time series. Moreover, we prove that when the series exhibit some additional structure like periodicity or smoothness, it is possible to improve on the classical rates of convergence.Acknowledgements. The authors gratefully acknowledge Maxime Ossonce for discussions which helped to improve the paper. The first author was working at CREST, EN-SAE Paris when this paper was written; he gratefully acknowledges financial support from Labex ECODEC (ANR-11-LABEX-0047).