Zhijie Xiao is a Professor of Economics at Boston College. He has been teaching at the University of Illinois at Urbana-Champaign after he got his Ph.D in economics at Yale University in 1997. Xiao received the Multa Scripsit Award from Econometric Theory in 2002 and the Plura Scripsit Award from the same journal in 2013. He is a Fellow of the Journal of Econometrics and has served as an Associate Editor for JASA and the Econometrics Journal. He is currently an Associate Editor of Econometric Theory. Zhijie Xiao has published over 100 articles on various topics in econometrics and empirical finance, including time series analysis, quantile regression, operational research, and semiparametric and nonparametric models.

Abstract:

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 real data application are given to validate our theory and algorithm.