  Initially designed for independent datas, low-rank matrix completion was
successfully applied in many domains to the reconstruction of partially
observed high-dimensional time series. However, there is a lack of theory to
support the application of these methods to dependent datas. In this paper, we
propose a general model for multivariate, partially observed time series. We
show that the least-square method with a rank penalty leads to reconstruction
error of the same order as for independent datas. Moreover, when the time
series has some additional properties such as perdiodicity or smoothness, the
rate can actually be faster than in the independent case.
