In-Fill Asymptotic Distribution of the Change Point Estimator when Estimating Breaks One at a Time

Abstract

Abstract In this study, we investigate the least squares (LS) estimator of a structural change point by the in-fill asymptotic theory, which has been recently used by Jiang, Wang, and Yu (2018. “New Distribution Theory for the Estimation of Structural Break Point in Mean.” Journal of Econometrics 205 (1): 156–76; 2020. “In-Fill Asymptotic Theory for Structural Break Point in Autoregressions.” Econometric Reviews 40 (4): 359–86), when the model with two structural changes is estimated as the model with only a one-time structural change. We, hence, show that the finite sample distribution of the estimator of the first break has four peaks, which is different from the classical long-span asymptotic distribution, which contains only one peak. Conversely, the in-fill asymptotic distribution of the estimator has four peaks and can approximate the finite sample distribution very well. We also demonstrate that the estimator is consistent in the in-fill asymptotic framework with a relatively large magnitude of the break. In the latter case, the finite sample distribution of the estimator has only one peak and is well approximated by both the in-fill and long-span asymptotic theory.