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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.

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

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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. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    3. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
    4. 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.
    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. Schmidt, P., 1988. "Dickey-Fuller Tests With Drift," Papers 8717, Michigan State - Econometrics and Economic Theory.
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Pierre St-Amant, 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. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    4. Perron, Pierre, 1992. "Racines unitaires en macroéconomie : le cas d’une variable," L'Actualité Economique, Société Canadienne de Science Economique, vol. 68(1), pages 325-356, mars et j.
    5. María del Mar Sánchez de la Vega & Arielle Beyaert, 1994. "Los contrastes de raiz unitaria: una panorámica," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 1, pages 109-154, Junio.
    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 333-364, Oct.-Dec..
    7. 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.
    8. Martin B. Schmidt & David J. Berri, 2005. "Concentration of Playing Talent," Journal of Sports Economics, , vol. 6(4), pages 412-419, November.
    9. 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.
    10. 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.
    11. 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.
    12. 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, Boston, Massachusetts 235792, Agricultural and Applied Economics Association.
    13. 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.
    14. Payne, James E. & Vizek, Maruška & Lee, Junsoo, 2017. "Is there convergence in per capita renewable energy consumption across U.S. States? Evidence from LM and RALS-LM unit root tests with breaks," Renewable and Sustainable Energy Reviews, Elsevier, vol. 70(C), pages 715-728.
    15. Gundlach, Erich, 1992. "Testing growth theories: Time series evidence," Kiel Working Papers 516, Kiel Institute for the World Economy (IfW Kiel).
    16. Paqué, Karl-Heinz, 1991. "Structural wage rigidity in West Germany 1950-1989: Some new econometric evidence," Kiel Working Papers 489, Kiel Institute for the World Economy (IfW Kiel).
    17. 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.
    18. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation for Research in Economics, Yale University.
    19. Schmidt, Peter & Lee, Junsoo, 1991. "A modification of the Schmidt-Phillips unit root test," Economics Letters, Elsevier, vol. 36(3), pages 285-289, July.
    20. Gil-Alana, Luis A. & Cunado, Juncal & Gupta, Rangan, 2017. "Evidence of persistence in U.S. short and long-term interest rates," Journal of Policy Modeling, Elsevier, vol. 39(5), pages 775-789.
    21. 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.
    22. Catherine Doz & Pierre Malgrange, 1992. "Modèles VAR et prévisions à court terme," Économie et Prévision, Programme National Persée, vol. 106(5), pages 109-122.
    23. Hany Fahmy, 2021. "A Reappraisal of the Prebisch-Singer Hypothesis Using Wavelets Analysis," JRFM, MDPI, vol. 14(7), pages 1-17, July.
    24. 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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