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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. Peter C.B. Phillips, 1995. "Unit Root Tests," Cowles Foundation Discussion Papers 1104, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  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. 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.
  6. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March.
  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. 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..
  9. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  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. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  12. 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.
  13. 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.
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Citations

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Cited by:
  1. Peter C. B. Phillips, 2009. "Bootstrapping I(1) Data," Cowles Foundation Discussion Papers 1689, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  4. 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.
  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. 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.
  7. 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.
  8. 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.
  9. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
  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. 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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