Distribution estimation and change-point detection for time series via DNN-based GANs

The generative adversarial networks (GANs) have recently been applied to estimating the distribution of independent and identically distributed data, and got excellent performances. In this paper, we use the blocking technique to demonstrate the effectiveness of GANs for estimating the distribution of stationary time series. Theoretically, we obtain 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 put forward an algorithm for detecting the change-point in time series. We simulate in our first experiment a stationary time series by the multivariate autoregressive model to test our GAN estimator, while the second experiment is to use our proposed algorithm to detect the change-point in a time series sequence. Both perform very well. The third experiment is to use our GAN estimator to learn the distribution of a real financial time series data, which is not stationary, we can see from the experiment results that our estimator cannot match the distribution of the time series very well but give the right changing tendency.