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Testing forUnit Root in the Presence of Deterministic Trends

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  • Schmidt, P.
  • Phillips, P.C.B.

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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Suggested Citation

  • Schmidt, P. & Phillips, P.C.B., 1990. "Testing forUnit Root in the Presence of Deterministic Trends," Papers 8904, Michigan State - Econometrics and Economic Theory.
    • Handle: RePEc:fth:mistet:8904
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Pierre St-Amant, 1996. "Decomposing U.S. Nominal Interest Rates into Expected Inflation and Ex Ante Real Interest Rates Using Structural VAR Methodology," Macroeconomics 9602004, University Library of Munich, Germany.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation for Research in Economics, Yale University.
    11. 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.
    12. Schmidt, Peter & Lee, Junsoo, 1991. "A modification of the Schmidt-Phillips unit root test," Economics Letters, Elsevier, vol. 36(3), pages 285-289, July.
    13. 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.
    14. Pierre Perron, 1992. "Racines unitaires en macroéconomie : le cas d’une variable," L'Actualité Economique, Société Canadienne de Science Economique, vol. 68(1), pages 325-356.
    15. 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.
    16. 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..
    17. 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.
    18. Martin B. Schmidt & David J. Berri, 2005. "Concentration of Playing Talent," Journal of Sports Economics, , vol. 6(4), pages 412-419, November.
    19. Gundlach, Erich, 1992. "Testing growth theories: Time series evidence," Kiel Working Papers 516, Kiel Institute for the World Economy.
    20. 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.
    21. 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.
    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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