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Testing for a Unit Root in the Presence of a Maintained Trend

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Sam Ouliaris (National U. of Singapore)
Joon Y. Park (Cornell University)

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Abstract

This paper develops statistics for detecting the presence of a unit root in time series data against the alternative stationarity. Unlike most existing procedures, the new tests allow for deterministic trend polynomials in the maintained hypothesis. They may be used to discriminate between unit root nonstationarity and processes which are stationary around a deterministic polynomial trend. The tests allow for both forms of nonstationarity under the null hypothesis. Moreover, the tests allow for a wide class of weakly dependent and possibly heterogenously distributed procedures. We illustrate the use of the new tests by applying them to a number of models of macroeconomic behavior.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 880.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 40 pages
Date of creation: Jun 1988
Date of revision:
Publication status: Published in B. Raj, ed., Advances in Econometrics and Modelling, 1989, pp. 7-28
Handle: RePEc:cwl:cwldpp:880

Note: CFP 756.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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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 roots; stationarity; time series; deterministic trend; 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. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-54, November. [Downloadable!] (restricted)
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  2. Corbae, Dean & Ouliaris, Sam, 1986. "Robust tests for unit roots in the foreign exchange market," Economics Letters, Elsevier, vol. 22(4), pages 375-380. [Downloadable!] (restricted)
  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
    Other versions:
  4. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation, Yale University, revised Feb 1987. [Downloadable!]
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  5. John Y. Campbell & N. Gregory Mankiw, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," NBER Working Papers 2169, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. Campbell, John Y & Mankiw, N Gregory, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 857-80, November. [Downloadable!] (restricted)
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  7. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
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  8. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-51, May. [Downloadable!] (restricted)
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  9. Perron, P., 1986. "Trends and Random Walks in Macroeconomic Time Series: Further Evidence From a New Approach," Cahiers de recherche 8650, Universite de Montreal, Departement de sciences economiques.
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  10. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-11, August. [Downloadable!] (restricted)
  11. 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)
  12. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October. [Downloadable!] (restricted)
Full references

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. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Technical Working Papers 0100, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    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. Junsoo Lee & John A. List & Mark Strazicich, 2005. "Nonrenewable Resource Prices: Deterministic or Stochastic Trends?," NBER Working Papers 11487, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Dean Corbea & Sam Ouliaris & Peter C.B. Phillips, 1991. "A Reexamination of the Consumption Function Using Frequency Domain Regressors," Cowles Foundation Discussion Papers 997, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Wang, Dabin & Tomek, William G., 2004. "Commodity Prices And Unit Root Tests," 2004 Annual meeting, August 1-4, Denver, CO 20141, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  6. Martin B. Schmidt, 2006. "On the evolution of competition: an application of nonlinear tests," Applied Economics, Taylor and Francis Journals, vol. 38(1), pages 1-12, January. [Downloadable!] (restricted)
  7. Martin Schmidt, 2009. "The nonlinear behavior of competition: the impact of talent compression on competition," Journal of Population Economics, Springer, vol. 22(1), pages 57-74, January. [Downloadable!] (restricted)
  8. He, Changli & Sandberg, Rickard, 2005. "Dickey-Fuller Type of Tests against Nonlinear Dynamic Models," Working Paper Series in Economics and Finance 580, Stockholm School of Economics. [Downloadable!]
  9. Peter C.B. Phillips & In Choi, 1989. "Testing for a Unit Root by Generalized Least Squares Methods in the Time and Frequency Domains," Cowles Foundation Discussion Papers CFP 899, Cowles Foundation, Yale University. [Downloadable!]
  10. Juan Carlos Cuestas, 2007. "Purchasing Power Parity In Central And Eastern European Countries: An Analysis Of Unit Roots And Nonlinearities," Working Papers. Serie AD 2007-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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  11. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation, Yale University. [Downloadable!]
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  12. HOLMES, Mark J, 2008. "Non-Linear Trend Stationarity And Co-Trending In Latin American Real Exchange Rates," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 8(1), pages 107-118. [Downloadable!] (restricted)
  13. David T. Griffiths, 2004. "The big problem of forecasting small change," Applied Economics, Taylor and Francis Journals, vol. 36(19), pages 2195-2207, September. [Downloadable!] (restricted)
  14. 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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