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An ADF Coefficient Test for a Unit Root in ARMA Models of Unknown Order with Empirical Applications to the U.S. Economy

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Abstract

This paper proposes an ADF coefficient test for detecting the presence of a unit root in ARMA models of unknown order. Our approach is fully parametric. When the time series has an unknown deterministic trend, we propose a modified version of the ADF coefficient test based on quasi-differencing in the construction of the detrending regression as in Elliot, Rothenberg and Stock (1996). The limit distributions of these test statistics are derived. Empirical applications of these tests for common macroeconomic time series in the US economy are reported and compared with the usual ADF t-test.

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File URL: http://cowles.econ.yale.edu/P/cd/d11b/d1161.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1161.

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Length: 18 pages
Date of creation: Sep 1997
Date of revision:
Publication status: Published in Econometrics Journal (1988), 1(2): 27-43
Handle: RePEc:cwl:cwldpp:1161

Note: CFP 1105.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  2. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
  3. Peter C.B. Phillips, 1995. "Unit Root Tests," Cowles Foundation Discussion Papers 1104, Cowles Foundation for Research in Economics, Yale University.
  4. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  5. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
  6. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
  7. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
  8. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
  9. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
  10. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation for Research in Economics, Yale University.
  11. 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.
  12. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
  13. DeJong, David N & Whiteman, Charles H, 1991. "The Temporal Stability of Dividends and Stock Prices: Evidence from the Likelihood Function," American Economic Review, American Economic Association, vol. 81(3), pages 600-617, June.
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Citations

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Cited by:
  1. Smeekes Stephan, 2009. "Detrending Bootstrap Unit Root Tests," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
  3. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
  4. Peter C. B. Phillips, 2009. "Bootstrapping I(1) Data," Cowles Foundation Discussion Papers 1689, Cowles Foundation for Research in Economics, Yale University.
  5. Westerlund, Joakim, 2006. "Testing for Error Correction in Panel Data," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Cheng, Ka Ming & Durmaz, Nazif & Kim, Hyeongwoo & Stern, Michael L., 2012. "Hysteresis vs. natural rate of US unemployment," Economic Modelling, Elsevier, vol. 29(2), pages 428-434.
  7. Phillips, Peter C. B., 2002. "New unit root asymptotics in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 111(2), pages 323-353, December.
  8. Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2013. "Unemployment Rate Hysteresis and the Great Recession: Exploring the Metropolitan Evidence," Working papers 2013-19, University of Connecticut, Department of Economics.
  9. John M. Roberts & Norman J. Morin, 1999. "Is hysteresis important for U.S. unemployment?," Finance and Economics Discussion Series 1999-56, Board of Governors of the Federal Reserve System (U.S.).
  10. George, Halkos & Ilias, Kevork, 2005. "Το Υπόδειγμα Τυχαίου Περιπάτου Με Αυτοπαλίνδρομα Σφάλματα
    [The random walk model with autoregressive errors]
    ," MPRA Paper 33312, University Library of Munich, Germany.
  11. David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2007. "Testing for a unit root when uncertain about the trend [Revised to become 07/03 above]," Discussion Papers 06/03, University of Nottingham, Granger Centre for Time Series Econometrics.

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