Bai, Jushan (1993): Least squares estimation of a shift in linear processes. Published in: Journal of Time Series Analysis , Vol. 15, No. 5 (September 1994): pp. 453472.

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Abstract
This paper considers a mean shift with an unknown shift point in a linear process and estimates the unknown shift point (change point) by the method of least squares. Preshift and postshift means are estimated concurrently with the change point. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained when the magnitude of shift is small. It is shown that serial correlation affects the variance of the change point estimator via the sum of the coefficients (impulses) of the linear process. When the underlying process is an ARMA, a mean shift causes overestimation of its order. A simple procedure is suggested to mitigate the bias in order estimation.
Item Type:  MPRA Paper 

Original Title:  Least squares estimation of a shift in linear processes 
Language:  English 
Keywords:  Mean shift; linear processes; change point; rate of convergence; order estimation; generalized residuals 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  32878 
Depositing User:  Jushan Bai 
Date Deposited:  21. Aug 2011 03:06 
Last Modified:  13. Feb 2013 07:32 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/32878 