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 use the blocking technique to demonstrate the effectiveness of GANs for estimating the 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. Based on our theoretical analysis, we propose an algorithm for estimating the change point in time series distribution. The two main results are verified by two Monte Carlo experiments respectively, one is to estimate the joint stationary distribution of $5$-tuple samples of a 20 dimensional AR(3) model, the other is about estimating the change point at the combination of two different stationary time series. A real world empirical application to the human activity recognition dataset highlights the potential of the proposed methods.

翻译：生成对抗网络（GANs）近期被应用于独立同分布数据的分布估计，并引起了广泛的研究关注。本文利用分块技术，证明了GANs在估计平稳时间序列分布方面的有效性。在理论上，我们推导了基于深度神经网络（DNN）的GANs估计器对时间序列平稳分布的非渐近误差界。基于理论分析，我们提出了一种用于估计时间序列分布变点的算法。两个主要结果分别通过两个蒙特卡洛实验进行验证：一个实验用于估计20维AR(3)模型中5元组样本的联合平稳分布；另一个实验用于估计两种不同平稳时间序列组合的变点。对人类活动识别数据集的实证应用凸显了所提方法的潜力。