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Powerful Tests of Structural Change That are Robust to Strong Serial Correlation


  • Ozgen Sayginsoy
  • Tim Vogelsang


This paper proposes powerful and serial correlation robust test statistics that can be used to test for the presence of structural change in the trend function of a univariate time series. Four models are analyzed, each model corresponding to a different way in which a trend break might occur. Given a model, the proposed tests are designed to detect a single break at an unknown date. The tests do not require the knowledge of the form of serial correlation in the data, and they are made robust to the presence of highly persistent serial correlation and a unit root in the errors by using a more comprehensive version of the scaling factor approach of Vogelsang (1998b). The tests utilize the popular nonparametric kernel variance estimators. The fixed-bandwidth asymptotic framework, proposed by Kiefer and Vogelsang (2003), is used to approximate the effects of the variance estimators on the test statistics. The fixed-bandwidth framework makes possible the choice of kernel and bandwidth that deliver tests with maximal asymptotic power within a specific class of tests. For each of the proposed tests, concrete and specific recommendations are made for the bandwidth and kernel to be used in practice. The recommended tests are shown to have good finite sample size and power properties.

Suggested Citation

  • 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.
  • Handle: RePEc:nya:albaec:04-08

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    References listed on IDEAS

    1. Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
    2. Ozgen Sayginsoy, 2004. "Powerful and Serial Correlation Robust Tests of the Economic Convergence Hypothesis," Discussion Papers 04-07, University at Albany, SUNY, Department of Economics.
    3. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
    6. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    7. Vogelsang, Timothy J., 1997. "Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series," Econometric Theory, Cambridge University Press, vol. 13(06), pages 818-848, December.
    8. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    9. Tanaka, Katsuto, 1990. "Testing for a Moving Average Unit Root," Econometric Theory, Cambridge University Press, vol. 6(04), pages 433-444, December.
    10. Chu, Chia-Shang James & White, Halbert, 1992. "A Direct Test for Changing Trend," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 289-299, July.
    11. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    12. 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.
    13. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    14. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-1369, November.
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    16. Chen, Chung & Tiao, George C, 1990. "Random Level-Shift Time Series Models, ARIMA Approximations, and Level-Shift Detection," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 83-97, January.
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    Cited by:

    1. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Testing For A Unit Root In The Presence Of A Possible Break In Trend," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1545-1588, December.
    2. Xu, Ke-Li, 2016. "Multivariate trend function testing with mixed stationary and integrated disturbances," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 38-57.
    3. Crafts, Nicholas & Mills, Terence C., 2009. "From Malthus to Solow: How did the Malthusian economy really evolve?," Journal of Macroeconomics, Elsevier, vol. 31(1), pages 68-93, March.
    4. Nuno Sobreira & Luis C. Nunes, 2016. "Tests for Multiple Breaks in the Trend with Stationary or Integrated Shocks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 394-411, June.

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