SMU SOE Seminar (Oct 30, 2016): In-fill Asymptotic Theory for Structural Break Point in Autoregression: A Unified Theory

    Based on the Girsanov theorem, this paper obtains the exact distribution of the maximum likelihood estimator of the structural break point in the Ornstein--Uhlenbeck process when a continuous record is available. The exact distribution is asymmetric and tri-modal, regardless of the location of the true break point. These two properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in autoregression (AR). The paper then develops an in-fill asymptotic theory for the LS estimator of the structural break point in AR. The in-fill asymptotic distribution is asymmetric and tri-modal and depends on the initial condition. It delivers good approximations to the finite sample distribution. Unlike the long-span asymptotic theory where the limiting distribution and sometimes even the rate of convergence depend on the underlying AR roots, the in-fill asymptotic theory is continuous in the underlying roots and, hence, offers a unified theory for making inference about the break point. Monte Carlo studies show that the in-fill asymptotic theory performs better than the existing tailor-made asymptotic theory in all cases considered.

JEL Classification: C11; C46