State-domain change point detection for nonlinear time series regression

Change point detection in time series has attracted substantial interest, but most of the existing results have been focused on detecting change points in the time domain. This paper considers the situation where nonlinear time series have potential change points in the state domain. We apply a density-weighted anti-symmetric kernel function to the state domain and therefore propose a nonparametric procedure to test the existence of change points. When the existence of change points is affirmative, we further introduce an algorithm to estimate the number of change points together with their locations. Theoretical results of the proposed detection and estimation procedures are given and a real dataset is used to illustrate our methods. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

Change point detection in time series has focused on the time domain, but this paper considers potential change points in the state domain of nonlinear time series. A nonparametric procedure is proposed using a density-weighted anti-symmetric kernel function to test the existence of change points. An algorithm is also introduced to estimate the number and locations of change points when they are confirmed to exist. Theoretical results and a real dataset are provided to illustrate the proposed methods.