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

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  • Ozgen Sayginsoy
  • Tim Vogelsang

Abstract

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.

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Bibliographic Info

Paper provided by University at Albany, SUNY, Department of Economics in its series Discussion Papers with number 04-08.

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Date of creation: 2004
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Handle: RePEc:nya:albaec:04-08

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Postal: Department of Economics, BA 110 University at Albany State University of New York Albany, NY 12222 U.S.A.
Phone: (518) 442-4735
Fax: (518) 442-4736

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Postal: Department of Economics, BA 110 University at Albany State University of New York Albany, NY 12222 U.S.A.
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Web: http://www.albany.edu/economics/research/workingp/index.shtml

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References

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  1. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "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?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  2. 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 289-99, July.
  3. Bunzel, Helle & Vogelsang, Timothy J., 2003. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis," Staff General Research Papers 10353, Iowa State University, Department of Economics.
  4. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  5. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
  6. 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.
  7. Tanaka, Katsuto, 1990. "Testing for a Moving Average Unit Root," Econometric Theory, Cambridge University Press, vol. 6(04), pages 433-444, December.
  8. 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.
  9. 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.
  10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  11. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November.
  12. 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.
  13. 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.
  14. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  15. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. 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.
  2. 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.
  3. Sobreira, Nuno & Nunes, Luis C., 2012. "Tests for Multiple Breaks in the Trend with Stationary or Integrated Shocks," Insper Working Papers wpe_290, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.

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