Statistical analysis of Wasserstein GANs with applications to time series forecasting
This work provides theoretical foundations for WGANs in time-dependent settings, which is incremental for researchers in statistical machine learning and time series analysis.
The authors developed statistical theory for Wasserstein GANs under dependent data, proving bounds on excess Bayes risk and weak convergence to enable confidence intervals, and applied it to high-dimensional time series forecasting with simulations and real temperature data.
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.