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Title: In-fill asymptotic theory for structural breakpoint in autoregression: A unified theory Authors:  Xiaohu Wang - The Chinese University of Hong Kong (Hong Kong) [presenting]
Liang Jiang - Singapore Management University (Singapore)
Jun Yu - Singapore Management University (Singapore)
Abstract: The exact distribution of the maximum likelihood estimator of structural break points in the Ornstein Uhlenbeck process is studied when a continuous record is available. The exact distribution is asymmetric, tri-modal, dependent on the initial condition. These three properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models. Motivated by these observations, an in-fill asymptotic theory is developed for the LS estimator of structural break point in the AR(1) coefficient. The in-fill asymptotic distribution is also asymmetric, trimodal, dependent on the initial condition, and delivers excellent approximations to the finite sample distribution. Unlike the long span asymptotic theory, which depends on the underlying AR root and hence is tailor made but is only available in a rather limited number of cases, the in-fill asymptotic theory is continuous in the underlying roots. Monte Carlo studies show that the in fill asymptotic theory performs better than the long-span asymptotic theory for cases where the long span theory is available and performs very well for cases where no long-span theory is available.