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On The Asymptotics Of Adf Tests For Unit Roots

  • Yoosoon Chang
  • Joon Park

In this paper, we derive the asymptotic distributions of Augmented-Dickey-Fuller (ADF) tests under very mild conditions. The tests were originally proposed and investigated by Said and Dickey (1984) for testing unit roots in finite-order ARMA models with i.i.d. innovations, and are based on a finite AR process of order increasing with the sample size. Our conditions are significantly weaker than theirs. In particular, we allow for general linear processes with martingale difference innovations, possibly having conditional heteroskedasticities. The linear processes driven by ARCH type innovations are thus permitted. The range for the permissible increasing rates for the AR approximation order is also much wider. For the usual t-type test, we only require that it increase at order o(n1/2) while they assume that it is of order o(nκ) for some κ satisfying 0 < κ ≤ 1/3.

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Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 21 (2002)
Issue (Month): 4 ()
Pages: 431-447

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Handle: RePEc:taf:emetrv:v:21:y:2002:i:4:p:431-447
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  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  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. 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.
  4. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
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