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 their number together with locations and show the convergence result on the estimation procedure. A real dataset of German daily confirmed cases of COVID-19 is used to illustrate our results.