Least squares estimation of a shift in linear processes
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. Pre-shift and post-shift 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.
|Date of creation:||16 Feb 1993|
|Date of revision:|
|Publication status:||Published in Journal of Time Series Analysis 5.15(1994): pp. 453-472|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
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- Donald W.K. Andrews, 1990.
"Tests for Parameter Instability and Structural Change with Unknown Change Point,"
Cowles Foundation Discussion Papers
943, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
- Ploberger, W & Kramer, W & Alt, R, 1989.
"A Modification of the CUSUM Test in the Linear Regression Model with Lagged Dependent Variables,"
Springer, vol. 14(2), pages 65-75.
- Krämer, Walter & Ploberger, Werner & Alt, Raimund, 1987. "A modification of the CUSUM test in the linear regression model with lagged dependent variables," Hannover Economic Papers (HEP) dp-104, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
- Bhattacharya, P.K., 1987. "Maximum likelihood estimation of a change-point in the distribution of independent random variables: General multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 183-208, December.
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