  Multivariate time series exhibit two types of dependence: across variables
and across time points. Vine copulas are graphical models for the dependence
and can conveniently capture both types of dependence in the same model. We
derive the maximal class of graph structures that guarantee stationarity under
a natural and verifiable condition called translation invariance. We propose
computationally efficient methods for estimation, simulation, prediction, and
uncertainty quantification and show their validity by asymptotic results and
simulations. The theoretical results allow for misspecified models and, even
when specialized to the iid case, go beyond what is available in the
literature. Their proofs are based on new results for general semiparametric
method-of-moment estimators, which shall be of independent interest. The new
model class is illustrated by an application to forecasting returns of a
portfolio of 20 stocks, where they show excellent forecast performance. The
paper is accompanied by an open source software implementation.
