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.
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