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An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy

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  • ZHIJE XIAO
  • PETER C.B. PHILLIPS

Abstract

This paper proposes an Augmented Dickey-Fuller (ADF) coefficient test for detecting the presence of a unit root in autoregressive moving average (ARMA) models of unknown order. Although the limit distribution of the coefficient estimate depends on nui-sance parameters, a simple transformation can be applied to eliminate the nuisance parameter asymptotically, providing an ADF coefficient test for this case. 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 Elliott et al. (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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Bibliographic Info

Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 1 (1998)
Issue (Month): RegularPapers ()
Pages: 27-43

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Handle: RePEc:ect:emjrnl:v:1:y:1998:i:regularpapers:p:27-43

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Related research

Keywords: ADF test; ARMA process; Unit root test.;

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References

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  1. 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.
  2. 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.
  3. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  4. Eugene Canjels & Mark W. Watson, 1994. "Estimating deterministic trends in the presence of serially correlated errors," Working Paper Series, Macroeconomic Issues 94-19, Federal Reserve Bank of Chicago.
  5. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
  6. 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.
  7. 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.
  8. Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis.
  9. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  10. 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.
  11. 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.
  12. 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.
  13. Peter C.B. Phillips, 1995. "Unit Root Tests," Cowles Foundation Discussion Papers 1104, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. 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.
  2. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
  3. 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.
  4. Peter C.B. Phillips, 1998. "New Unit Root Asymptotics in the Presence of Deterministic Trends," Cowles Foundation Discussion Papers 1196, Cowles Foundation for Research in Economics, Yale University.
  5. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Unit root testing in practice: dealing with uncertainty over the trend and initial condition," Discussion Papers 07/03, University of Nottingham, Granger Centre for Time Series Econometrics.
  6. Peter C. B. Phillips, 2009. "Bootstrapping I(1) Data," Cowles Foundation Discussion Papers 1689, Cowles Foundation for Research in Economics, Yale University.
  7. 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.
  8. 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).
  9. 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.
  10. Ka Ming Cheng & Nazif Durmaz & Hyeongwoo Kim & Michael Stern, 2011. "Hysteresis vs. Natural Rate of US Unemployment," Auburn Economics Working Paper Series auwp2011-01, Department of Economics, Auburn University.
  11. 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.).

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