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GLS detrending, efficient unit root tests and structural change

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  • Perron, Pierre
  • Rodriguez, Gabriel

Abstract

The asymptotic power envelope is derived for point-optimal tests of a unit root in the autoregressive representation of a Gaussian time series. The authors propose a family of tests whose asymptotic power functions are tangent to the power envelope at one point and are never far below. When the series has an unknown mean or linear trend, commonly used tests are found to be dominated by members of the family of point-optimal invariant tests. The authors propose a modified version of the Dickey-Fuller t test which has desirable size properties and substantially improved power when an unknown mean or trend is present. Copyright 1996 by The Econometric Society.
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  • Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
  • Handle: RePEc:eee:econom:v:115:y:2003:i:1:p:1-27
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    1. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Chapters,in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220 National Bureau of Economic Research, Inc.
    2. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    3. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    4. Christiano, Lawrence J. & Eichenbaum, Martin, 1990. "Unit roots in real GNP: Do we know, and do we care?," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 32(1), pages 7-61, January.
    5. John Y. Campbell & N. Gregory Mankiw, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 857-880.
    6. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    7. Perron, Pierre & Ng, Serena, 1998. "An Autoregressive Spectral Density Estimator At Frequency Zero For Nonstationarity Tests," Econometric Theory, Cambridge University Press, vol. 14(05), pages 560-603, October.
    8. Campbell, John Y & Mankiw, N Gregory, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 77(2), pages 111-117, May.
    9. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
    10. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    11. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-250, July.
    12. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 797-814.
    13. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    14. 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.
    15. Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
    16. Matthew Shapiro & Mark Watson, 1988. "Sources of Business Cycles Fluctuations," NBER Chapters,in: NBER Macroeconomics Annual 1988, Volume 3, pages 111-156 National Bureau of Economic Research, Inc.
    17. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    18. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    19. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    20. 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.
    21. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    22. 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.
    23. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • 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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