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

TL;DR

This paper demonstrates the effectiveness of DNN-based GANs for estimating stationary time series distributions and detecting change points, supported by theoretical error bounds and empirical experiments.

Contribution

It introduces a non-asymptotic error bound for DNN-GANs in time series distribution estimation and proposes a change point detection algorithm based on this theory.

Findings

DNN-GANs effectively estimate joint distributions of high-dimensional time series.

The proposed change point detection algorithm accurately identifies distribution shifts.

Empirical results validate the theoretical error bounds and method effectiveness.

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 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.