Estimating multiple breaks one at a time

Sequential (one-by-one) rather than simultaneous estimation of multiple breaks is investigated in this paper. The advantage of this method lies in its computational savings and its robustness to misspecification in the number of breaks. The number of least-squares regressions required to compute all of the break points is of order T, the sample size. Each estimated break point is shown to be consistent for one of the true ones despite underspecification of the number of breaks. More interestingly and somewhat surprisingly, the estimated break points are shown to be T-consistent, the same rate as the simultaneous estimation. Limiting distributions are also derived. Unlike simultaneous estimation, the limiting distributions are generally not symmetric and are influenced by regression parameters of all regimes. A simple method is introduced to obtain break point estimators that have the same limiting distributions as those obtained via simultaneous estimation. Finally, a procedure is proposed to consistently estimate the number of breaks.