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Testing for a Unit Root in the Presence of Deterministic Trends

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Abstract

This paper provides a new unit root test based on an alternative parameterization which has previously been considered by Bhargava (1986). This parameterization allows for trend under both the null and the alternative, without introducing any parameters that are irrelevant under either. This is not so in the Dickey-Fuller parameterizations. The new test is extracted from the score or LM principle under the assumption that the errors are iid N(0, sigma squared (epsilon)), but our asymptotics hold under more general assumptions about the errors. Two forms of the test (a coefficient test and at t-test) are derived.

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File URL: http://cowles.econ.yale.edu/P/cd/d09a/d0933.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 933.

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Length: 37 pages
Date of creation: Oct 1989
Date of revision:
Publication status: Published in Oxford Bulletin of Economics and Statistics (1992), 54(3): 257-287
Handle: RePEc:cwl:cwldpp:933

Note: CFP 820.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Unit root; time series; random walk; co-integration;

References

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  1. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  2. West, Kenneth D., 1987. "A note on the power of least squares tests for a unit root," Economics Letters, Elsevier, vol. 24(3), pages 249-252.
  3. Schmidt, P., 1988. "Dickey-Fuller Tests With Drift," Papers 8717, Michigan State - Econometrics and Economic Theory.
  4. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  5. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  6. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  8. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
  9. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
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Citations

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Cited by:
  1. Eric Zivot & Peter C.B. Phillips, 1991. "A Bayesian Analysis of Trend Determination in Economic Time Series," Cowles Foundation Discussion Papers 1002, Cowles Foundation for Research in Economics, Yale University.
  2. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  3. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation for Research in Economics, Yale University.
  4. Phillips, P C B, 1991. "Bayesian Routes and Unit Roots: De Rebus Prioribus Semper Est Disputandum," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 435-73, Oct.-Dec..
  5. St-Amant, P., 1996. "Decomposing U.S. Nominal Interest Rates into Expected Inflation and Ex Ante Real Interest rates Using Structural VAR Methodology," Working Papers 96-2, Bank of Canada.
  6. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  7. Pierre Malgrange & Catherine Doz, 1992. "Modèles VAR et prévisions à court terme," Économie et Prévision, Programme National Persée, vol. 106(5), pages 109-122.
  8. Philippe Gudin de Vallerin & Stéphane Capet, 1993. "Fonctions d'importations et d'exportations : l'apport de la théorie économétrique récente," Économie et Prévision, Programme National Persée, vol. 107(1), pages 15-36.

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