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Testing for a Unit Root in the Presence of Deterministic Trends



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.

Suggested Citation

  • Peter C.B. Phillips & Peter Schmidt, 1989. "Testing for a Unit Root in the Presence of Deterministic Trends," Cowles Foundation Discussion Papers 933, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:933
    Note: CFP 820.

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    References listed on IDEAS

    1. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
    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. repec:bla:restud:v:57:y:1990:i:1:p:99-125 is not listed on IDEAS
    5. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-1269, September.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    8. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
    9. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    10. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    11. 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.
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    Cited by:

    1. St-Amant, P., 1996. "Decomposing U.S. Nominal Interest Rates into Expected Inflation and Ex Ante Real Interest rates Using Structural VAR Methodology," Staff Working Papers 96-2, Bank of Canada.
    2. Noriega-Muro, Antonio, 1995. "Asymptotic theory of statistics form unit root test regressions when the alternative is a breaking-trend-stationary model," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 10(1), pages 29-65.
    3. 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 333-364, Oct.-Dec..
    4. Stéphane Capet & Philippe Gudin de Vallerin, 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.
    5. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    6. Philippe Gudin & Antoine Magnier & Nicolas Ponty, 1991. "Taux d'intérêt : une asymétrie moins forte," Économie et Statistique, Programme National Persée, vol. 246(1), pages 55-63.
    7. Changli He & Rickard Sandberg, 2006. "Dickey-Fuller Type of Tests against Nonlinear Dynamic Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 835-861, December.
    8. Pena-Levano, Luis M & Foster, Kenneth, 2016. "Efficiency gains in commodity forecasting using disaggregated levels versus more aggregated predictions," 2016 Annual Meeting, July 31-August 2, 2016, Boston, Massachusetts 235792, Agricultural and Applied Economics Association.
    9. Ben Salem, Melika & Jacques, Jean-Francois, 1999. "Contribution of aggregate and sectoral shocks to the dynamics of inventories:: An empirical study with French and American data," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 33-42, March.
    10. Yaya, OlaOluwa Simon & Gil-Alana, Luis Alberiko & Carcel, Hector, 2015. "Testing fractional persistence and non-linearities in the natural gas market: An application of non-linear deterministic terms based on Chebyshev polynomials in time," Energy Economics, Elsevier, vol. 52(PA), pages 240-245.
    11. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation for Research in Economics, Yale University.
    12. repec:eee:jpolmo:v:39:y:2017:i:5:p:775-789 is not listed on IDEAS
    13. 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.
    14. Catherine Doz & Pierre Malgrange, 1992. "Modèles VAR et prévisions à court terme," Économie et Prévision, Programme National Persée, vol. 106(5), pages 109-122.
    15. 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 435-473, Oct.-Dec..

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


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