  In this paper we consider the low-rank matrix completion problem with
specific application to forecasting in time series analysis. Briefly, the
low-rank matrix completion problem is the problem of imputing missing values of
a matrix under a rank constraint. We consider a matrix completion problem for
Hankel matrices and a convex relaxation based on the nuclear norm. Based on new
theoretical results and a number of numerical and real examples, we investigate
the cases when the proposed approach can work. Our results highlight the
importance of choosing a proper weighting scheme for the known observations.
