Abstract

In this paper, we investigate the change point estimator with the weighted objective function, which has been studied in Baek (2018), when the model has two structural breaks and is estimated one at a time. The finite sample distribution of the change point LS estimator is trimodal; it has peaks around the true break points and the end of the samples. We show that these peaks on the end points disappear when estimating the change point with the weighted objective function. The new estimator is consistent with either of the true ones and the convergence rate is the same as the rate of the traditional estimator in Bai (1997). However, when the limits of the objective function at the true break points are the same, the estimator does not necessarily converge in probability to the true break point. When the magnitude of the breaks shrinks, the new estimator converges to a unimodal and asymmetry distribution.