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Testing for a Unit Root in the Presence of Deterministic Trends

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Peter Schmidt (Michigan State University)

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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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Publisher Info
Paper provided by Cowles Foundation, 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

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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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.
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  2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January. [Downloadable!] (restricted)
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  5. Schmidt, P., 1988. "Dickey-Fuller Tests With Drift," Papers 8717, Michigan State - Econometrics and Economic Theory.
  6. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September. [Downloadable!] (restricted)
  7. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation, Yale University, revised Jul 1989. [Downloadable!]
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  8. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March. [Downloadable!] (restricted)
  9. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Blackwell Publishing, vol. 53(3), pages 369-84, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Peter C.B. Phillips, 1991. "Bayesian Routes and Unit Roots: de rebus prioribus semper est disputandum," Cowles Foundation Discussion Papers 986, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Peter C.B. Phillips, 1990. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Cowles Foundation Discussion Papers 950, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Eric Zivot & Peter C.B. Phillips, 1991. "A Bayesian Analysis of Trend Determination in Economic Time Series," Cowles Foundation Discussion Papers 1002, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation, Yale University. [Downloadable!]
  5. 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, Yale University. [Downloadable!]
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  6. Stéphane Gregoir & Guy Laroque, 1992. "La place des stocks dans les fluctuations conjoncturelles," Annales d'Economie et de Statistique, ADRES, issue 28, pages 02, Octobre-D. [Downloadable!]
  7. 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. [Downloadable!]
    Other versions:
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