Distribution estimation for time series via DNN-based GANs with an application to change-point estimation

The generative adversarial networks (GANs) have recently been applied to estimating the distribution of independent and identically distributed data, and have attracted a lot of research attention. In this paper, we demonstrate the effectiveness of GANs in estimating the joint distribution of stationary time series. Theoretically, we derive a non-asymptotic error bound for the Deep Neural Network (DNN)-based GANs estimator for the stationary distribution of the time series. Our approach is based on the blocking technique and the M -dependence approximation technique that divides the time series into interlacing blocks of equal size and then constructs independent blocks. Based on the theoretical analysis, we propose an algorithm for estimating the position of the change-point in a time series. Numerical results of Monte Carlo experiments and a real data application are given to validate our theory and algorithm.