  We propose a novel bootstrap procedure for dependent data based on Generative
Adversarial networks (GANs). We show that the dynamics of common stationary
time series processes can be learned by GANs and demonstrate that GANs trained
on a single sample path can be used to generate additional samples from the
process. We find that temporal convolutional neural networks provide a suitable
design for the generator and discriminator, and that convincing samples can be
generated on the basis of a vector of iid normal noise. We demonstrate the
finite sample properties of GAN sampling and the suggested bootstrap using
simulations where we compare the performance to circular block bootstrapping in
the case of resampling an AR(1) time series processes. We find that resampling
using the GAN can outperform circular block bootstrapping in terms of empirical
coverage.
