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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

  • ZHIJE XIAO
  • PETER C.B. PHILLIPS

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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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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  1. 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.
  2. 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.
  3. 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.
  4. Peter C.B. Phillips, 1995. "Unit Root Tests," Cowles Foundation Discussion Papers 1104, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  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. 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.
  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. 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.
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