IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v15y1994i5p453-472.html
   My bibliography  Save this article

Least Squares Estimation Of A Shift In Linear Processes

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.1994.tb00204.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.1994.tb00204.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, vol. 119(1), pages 19-44, March.
    2. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2012. "Inference regarding multiple structural changes in linear models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 281-302.
    3. Vogelsang, Timothy J., 1998. "Sources of nonmonotonic power when testing for a shift in mean of a dynamic time series," Journal of Econometrics, Elsevier, vol. 88(2), pages 283-299, November.
    4. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2008. "Inference regarding multiple structural changes in linear models estimated via two stage least squares," MPRA Paper 9251, University Library of Munich, Germany, revised 20 Jun 2008.
    5. Link, Albert N. & van Hasselt, Martijn, 2019. "On the transfer of technology from universities: The impact of the Bayh–Dole Act of 1980 on the institutionalization of university research," European Economic Review, Elsevier, vol. 119(C), pages 472-481.
    6. Ozgen Sayginsoy & Tim Vogelsang, 2004. "Powerful Tests of Structural Change That are Robust to Strong Serial Correlation," Discussion Papers 04-08, University at Albany, SUNY, Department of Economics.
    7. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    8. Otilia Boldea & Alastair Hall & Sanggohn Han, 2010. "Uncertainty, Entrepreneurship and the Organisation of Corruption," Centre for Growth and Business Cycle Research Discussion Paper Series 134, Economics, The University of Manchester.
    9. Casini, Alessandro & Perron, Pierre, 2022. "Generalized Laplace Inference In Multiple Change-Points Models," Econometric Theory, Cambridge University Press, vol. 38(1), pages 35-65, February.
    10. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation for Research in Economics, Yale University.
    11. Jin, Hao & Zhang, Jinsuo, 2010. "Subsampling tests for variance changes in the presence of autoregressive parameter shifts," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2255-2265, November.
    12. Sahbi FARHANI, 2012. "Tests of Parameters Instability: Theoretical Study and Empirical Analysis on Two Types of Models (ARMA Model and Market Model)," International Journal of Economics and Financial Issues, Econjournals, vol. 2(3), pages 246-266.
    13. Alessandro Casini & Pierre Perron, "undated". "Generalized Laplace Inference in Multiple Change-Points Models," Boston University - Department of Economics - Working Papers Series WP2018-012, Boston University - Department of Economics.
    14. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, vol. 109(2), pages 365-387, August.
    15. Otilia Boldea & Alastair Hall & Sanggohn Han, 2012. "Asymptotic Distribution Theory for Break Point Estimators in Models Estimated via 2SLS," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 1-33.
    16. Michael Greenstone & Rema Hanna, 2014. "Environmental Regulations, Air and Water Pollution, and Infant Mortality in India," American Economic Review, American Economic Association, vol. 104(10), pages 3038-3072, October.
    17. Joshy Easaw & Roberto Golinelli, 2022. "Professionals Inflation Forecasts: The Two Dimensions Of Forecaster Inattentiveness [“Sectoral and aggregate inflation dynamics in the euro area”]," Oxford Economic Papers, Oxford University Press, vol. 74(3), pages 701-720.
    18. Evangelos Charalambakis & Yiannis Dendramis & Elias Tzavalis, 2017. "On the determinants of NPLS: lessons from Greece," Working Papers 220, Bank of Greece.
    19. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.
    20. Anne Morrison Piehl & Suzanne J. Cooper & Anthony A. Braga & David M. Kennedy, 2003. "Testing for Structural Breaks in the Evaluation of Programs," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 550-558, August.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jtsera:v:15:y:1994:i:5:p:453-472. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.