Abstract

This study considers a model with a structural break in the disturbance and investigates the behavior of the change-point estimator. There are many studies for the break point estimation with the mean shift, and these studies assume that a variance in the error term is constant over time. In this paper, we demonstrate that, when the magnitude of the break in disturbance is small, the finite sample and asymptotic distributions of the estimator have three peaks at around the true break point and the beginning and end of the sample points and are asymmetry. The shape of these distributions is very similar to Jiang et al. (2018) which consider the mean shift model with a small shift under the in-fill asymptotic scheme.