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Least Squares Estimation Of A Shift In Linear Processes

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  • Jushan Bai

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 of the linear process. When the underlying process is autoregressive moving average, a mean shift causes overestimation of its order. A simple procedure is suggested to mitigate the bias in order estimation.

Suggested Citation

  • Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:5:p:453-472
    DOI: 10.1111/j.1467-9892.1994.tb00204.x
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    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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