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Based on the Girsanov theorem, this paper first obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and tri-modal, indicating that the estimator is seriously biased. These two properties are also found in the finite sample distribution of the least squares estimator of structural break point in the discrete time model. The paper then builds a continuous time approximation to the discrete time model and develops an in-fill asymptotic theory for the least squares estimator. The obtained in-fill asymptotic distribution is asymmetric and tri-modal and delivers good approximations to the finite sample distribution. In order to reduce the bias in the estimation of both the continuous time model and the discrete time model, a simulation-based method based on the indirect estimation approach is proposed. Monte Carlo studies show that the indirect estimation method achieves substantial bias reductions. However, since the binding function has a slope less than one, the variance of the indirect estimator is larger than that of the original estimator.


Structural break, Bias reduction, Indirect estimation, Exact distribution, In-fill asymptotics



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Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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