Estimation of change-points in linear and nonlinear time series models

This paper develops an asymptotic theory for estimated change-points in linear and nonlinear time series models. Based on a measurable objective function, it is shown that the estimated change-point converges weakly to the location of the maxima of a double-sided random walk and other estimated parameters are asymptotically normal. When the magnitude d of changed parameters is small, it is shown that the limiting distribution can be approximated by the known distribution as in Yao (1987, Annals of Statistics 15, 1321-1328). This provides a channel to connect our results with those in Picard (1985, Advances in Applied Probability 17, 841-867) and Bai, Lumsdaine, and Stock (1998, Review of Economic Studies 65, 395-432), where the magnitude of changed parameters depends on the sample size n and tends to zero as n →. The theory is applied for the self-weighted QMLE and the local QMLE of change-points in ARMA-GARCH/IGARCH models. A simulation study is carried out to evaluate the performance of these estimators in the finite sample.