  We propose a vector auto-regressive (VAR) model with a low-rank constraint on
the transition matrix. This new model is well suited to predict
high-dimensional series that are highly correlated, or that are driven by a
small number of hidden factors. We study estimation, prediction, and rank
selection for this model in a very general setting. Our method shows excellent
performances on a wide variety of simulated datasets. On macro-economic data
from Giannone et al. (2015), our method is competitive with state-of-the-art
methods in small dimension, and even improves on them in high dimension.
