In-fill asymptotic theory for structural break point in autoregression: A unified theory - JIANG, Liang (Institutional Knowledge at Singapore Management University, 2017)
This paper obtains the exact distribution of the maximum likelihood estimatorof structural break point in the OrnsteinñUhlenbeck process when a continuousrecord is available. The exact distribution is asymmetric, tri-modal, dependenton the initial condition. These three properties are also found in the önite sampledistribution of the least squares (LS) estimator of structural break point inautoregressive (AR) models. Motivated by these observations, the paper then developsan in-öll asymptotic theory for the LS estimator of structural break point inthe AR(1) coe¢ cient. The in-öll asymptotic distribution is also asymmetric, trimodal,dependent on the initial condition, and delivers excellent approximationsto the önite sample distribution. Unlike the long-span asymptotic theory, whichdepends on the underlying AR root and hence is tailor-made but is only availablein a rather limited number of cases, the in-öll asymptotic theory is continuousin the underlying roots. Monte Carlo studies show that the in-öll asymptotictheory performs better than the long-span asymptotic theory for cases where thelong-span theory is available and performs very well for cases where no long-spantheory is available