  We provide statistical theory for conditional and unconditional Wasserstein
generative adversarial networks (WGANs) in the framework of dependent
observations. We prove upper bounds for the excess Bayes risk of the WGAN
estimators with respect to a modified Wasserstein-type distance. Furthermore,
we formalize and derive statements on the weak convergence of the estimators
and use them to develop confidence intervals for new observations. The theory
is applied to the special case of high-dimensional time series forecasting. We
analyze the behavior of the estimators in simulations based on synthetic data
and investigate a real data example with temperature data. The dependency of
the data is quantified with absolutely regular beta-mixing coefficients.
