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Efficient Tests for an Autoregressive Unit Root

Listed author(s):
  • Elliott, Graham
  • Rothenberg, Thomas J
  • Stock, James H

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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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 64 (1996)
Issue (Month): 4 (July)
Pages: 813-836

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Handle: RePEc:ecm:emetrp:v:64:y:1996:i:4:p:813-36
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  13. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
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  17. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
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  19. Perron, P., 1994. "Further Evidence on Breaking Trend Functions in Macroeconomic Variables," Cahiers de recherche 9421, Universite de Montreal, Departement de sciences economiques.
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  21. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
  22. 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.
  23. 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.
  24. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
  25. 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.
  26. 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.
  27. 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.
  28. Schmidt, P. & Phillips, P.C.B., 1990. "Testing forUnit Root in the Presence of Deterministic Trends," Papers 8904, Michigan State - Econometrics and Economic Theory.
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