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

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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.

Suggested Citation

  • Peter C.B. Phillips & Sam Ouliaris & Joon Y. Park, 1988. "Testing for a Unit Root in the Presence of a Maintained Trend," Cowles Foundation Discussion Papers 880, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:880
    Note: CFP 756.
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d08/d0880.pdf
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    References listed on IDEAS

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    1. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-751, May.
    2. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
    3. John Y. Campbell & N. Gregory Mankiw, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 857-880.
    4. Campbell, John Y & Mankiw, N Gregory, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 77(2), pages 111-117, May.
    5. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332.
    8. 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.
    9. Corbae, Dean & Ouliaris, Sam, 1986. "Robust tests for unit roots in the foreign exchange market," Economics Letters, Elsevier, vol. 22(4), pages 375-380.
    10. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    11. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    12. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    13. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-511, August.
    14. 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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