Abstract
This article studies the identification problem in AR(1) models with a change in the AR parameter at an unknown time k 0. Consider the model where denotes the indicator function and is a sequence of i.i.d. random variables which are in the domain of attraction of the normal law with zero means and possibly infinite variances. Two cases were investigated: case (I) and case (II) where c is a fixed constant. We derived the limiting distributions of the least squares estimator of the break fraction τ 0() for the cases above under some mild conditions. The results showed that the change point (or k 0) is non identifiable for the aforementioned two cases by the least squares method. Monte Carlo experiments were conducted to examine the identification of τ 0 under finite sample situations. Our theoretical results are supported by the Monte Carlo experiments.
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