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Testing for a Shift in Mean without Having to Estimate Serial-Correlation Parameters

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  • Vogelsang, Timothy J

Abstract

Tests for detecting a shift in the mean of univariate time series that do not require estimation of serial-correlation parameters are proposed. The statistics are valid whether the errors are stationary or have a unit root. The date of the shift may be known or unknown. The statics are based on a simple transformation of the data and are functions of partial sums of the data. These so-called partial sum statistics are shown to be asymptotically invariant to serial-correlation parameters. The statistics are shown to have good size and power properties asymptotically and in finite samples.

Suggested Citation

  • Vogelsang, Timothy J, 1998. "Testing for a Shift in Mean without Having to Estimate Serial-Correlation Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 73-80, January.
    • Handle: RePEc:bes:jnlbes:v:16:y:1998:i:1:p:73-80
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    Cited by:

    1. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    2. Mikael Linden, 2002. "Trend model testing of growth convergence in 15 OECD countries, 1946-1997," Applied Economics, Taylor & Francis Journals, vol. 34(2), pages 133-142.
    3. Gerard O'Reilly & Karl Whelan, 2005. "Has Euro-Area Inflation Persistence Changed Over Time?," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 709-720, November.
    4. Serena Ng & Timothy Vogelsang, 2002. "Analysis Of Vector Autoregressions In The Presence Of Shifts In Mean," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 353-381.
    5. Nielsen, Morten Ørregaard, 2009. "A Powerful Test Of The Autoregressive Unit Root Hypothesis Based On A Tuning Parameter Free Statistic," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1515-1544, December.
    6. Harvey, David I. & Leybourne, Stephen J., 2015. "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 184(2), pages 262-279.
    7. David I. Harvey & Stephen J. Leybourne & Paul Newbold, 2004. "Tests for a Break in Level when the Order of Integration is Unknown," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(1), pages 133-146, February.
    8. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    9. László Kónya, 2020. "Did the unemployment rates converge in the EU?," Empirical Economics, Springer, vol. 59(2), pages 627-657, August.
    10. Jushan Bai & Josep Lluís Carrion-I-Silvestre, 2009. "Structural Changes, Common Stochastic Trends, and Unit Roots in Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(2), pages 471-501.
    11. Yannick Hoga, 2022. "Quantifying the data-dredging bias in structural break tests," Statistical Papers, Springer, vol. 63(1), pages 143-155, February.
    12. Bent Jesper Christensen & Robinson Kruse & Philipp Sibbertsen, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," CREATES Research Papers 2013-35, Department of Economics and Business Economics, Aarhus University.
    13. Lai, Kon S., 2008. "The puzzling unit root in the real interest rate and its inconsistency with intertemporal consumption behavior," Journal of International Money and Finance, Elsevier, vol. 27(1), pages 140-155, February.
    14. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December.
    15. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January.
    16. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
    17. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2006. "Modified tests for a change in persistence," Journal of Econometrics, Elsevier, vol. 134(2), pages 441-469, October.
    18. Morten Ø. Nielsen, 2008. "A Powerful Tuning Parameter Free Test Of The Autoregressive Unit Root Hypothesis," Working Paper 1175, Economics Department, Queen's University.
    19. David I. Harvey & Stephen J. Leybourne, 2014. "Break Date Estimation for Models with Deterministic Structural Change," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 623-642, October.
    20. Crainiceanu, Ciprian & Vogelsang, Timothy, 2001. "Spectral Density Bandwidth Choice: Source of Nonmonotonic Power for Tests of a Mean Shift in a Time Series," Working Papers 01-14, Cornell University, Center for Analytic Economics.
    21. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
    22. 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.

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