Change-point estimators with the weighted objective function when sequentially estimating breaks

Abstract

Change-point estimators based on a recently proposed weighted objective function are investigated, focusing on models with two structural breaks estimated sequentially. The asymptotic distributions of the first- and second-step estimators are examined under the long-span asymptotic scheme, which applies under large break sizes. It is shown that these distributions are generally unimodal and asymmetric. However, under small break sizes, the limiting distribution under the aforementioned scheme fails to accurately approximate the finite sample distribution. The first-step estimator’s finite sample distribution tends to exhibit two peaks, while the corresponding asymptotic distribution remains unimodal. This finite sample characteristic is better approximated under the in-fill asymptotic scheme.