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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.

Suggested Citation

  • Zhije Xiao & Peter C.B. Phillips, 1998. "An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 27-43.
    • Handle: RePEc:ect:emjrnl:v:1:y:1998:i:regularpapers:p:27-43
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    1. 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.
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    Cited by:

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    2. Joakim Westerlund, 2007. "Testing for Error Correction in Panel Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(6), pages 709-748, December.
    3. Phillips, Peter C.B., 2010. "Bootstrapping I(1) data," Journal of Econometrics, Elsevier, vol. 158(2), pages 280-284, October.
    4. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    5. 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.
    6. 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.
    7. 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(3), pages 587-636, June.
    8. Kindie, Getnet & Verbeke, Wim & Viaene, Jacques, 2006. "Stochastic Producer Prices and Shock Persistence in Agriculture: Implications for Food Policy and Price Information," Ethiopian Journal of Economics, Ethiopian Economics Association, vol. 12(2), pages 1-81, November.
    9. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    10. Norman J. Morin & John M. Roberts, 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.).
    11. Ahmed, Muhammad Ashfaq & Nawaz, Nasreen, 2023. "A Sufficient Statistical Test for Dynamic Stability," MPRA Paper 116684, University Library of Munich, Germany.
    12. 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.
    13. Jürgen Wolters & Uwe Hassler, 2006. "Unit root testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 43-58, March.
    14. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    15. Fathali Firoozi & Donald Lien, 2016. "A Modified ADF Test for Geometric ARMA Processes," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 15(2), pages 173-179, December.
    16. Emre Aylar & Stephan Smeekes & Joakim Westerlund, 2019. "Lag truncation and the local asymptotic distribution of the ADF test for a unit root," Statistical Papers, Springer, vol. 60(6), pages 2109-2118, December.
    17. 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.
    18. Mercedes Alda & Luis Ferruz, 2012. "Linear and nonlinear financial time series: evidence in a sample of pension funds in Spain and the United Kingdom," Applied Economics Letters, Taylor & Francis Journals, vol. 19(18), pages 1933-1937, December.
    19. Emmanuel E. Okoro & Lawrence U. Okoye & Ikechukwu S. Okafor & Tamunotonjo Obomanu & Ngozi Adeleye, 2021. "Impact of Production Sharing Contract Price Sliding Royalty: The case of Nigeria s Deepwater Operation," International Journal of Energy Economics and Policy, Econjournals, vol. 11(3), pages 261-268.

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