Statistical analysis of Wasserstein GANs with applications to time series forecasting

TL;DR

This paper develops statistical theory for Wasserstein GANs with dependent data, providing bounds, convergence results, and confidence intervals, especially applied to high-dimensional time series forecasting.

Contribution

It introduces a theoretical framework for WGANs with dependent observations, including excess risk bounds, weak convergence, and confidence intervals, with applications to time series forecasting.

Findings

Bounds for excess Bayes risk of WGAN estimators

Weak convergence and confidence intervals for estimators

Successful application to synthetic and real temperature data

Abstract

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.