  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.
