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Least squares estimation of a shift in linear processes

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  • Bai, Jushan

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. 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.

Suggested Citation

  • Bai, Jushan, 1993. "Least squares estimation of a shift in linear processes," MPRA Paper 32878, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:32878
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    References listed on IDEAS

    as
    1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    2. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    3. Ploberger, W & Kramer, W & Alt, R, 1989. "A Modification of the CUSUM Test in the Linear Regression Model with Lagged Dependent Variables," Empirical Economics, Springer, vol. 14(2), pages 65-75.
    4. 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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    More about this item

    Keywords

    Mean shift; linear processes; change point; rate of convergence; order estimation; generalized residuals;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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