The Asymptotic Size and Power of the Augmented Dickey-Fuller Test for a Unit Root
It is shown that the limiting distribution of the augmented Dickey-Fuller (ADF) test under the null hypothesis of a unit root is valid under a very general set of assumptions that goes far beyond the linear AR (âˆž) process assumption typically imposed. In essence, all that is required is that the error process driving the random walk possesses a spectral density that is strictly positive. Given that many economic time series are nonlinear, this extended result may have important applications. Furthermore, under the same weak assumptions, the limiting distribution of the ADF test is derived under the alternative of stationarity, and a theoretical explanation is given for the well-known empirical fact that the test's power is a decreasing function of the autoregressive order p used in the augmented regression equation. The intuitive reason for the reduced power of the ADF test as p tends to infinity is that the p regressors become asymptotically collinear.Â Â
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- Abadir, Karim M., 1993. "On the Asymptotic Power of Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 9(02), pages 189-221, April.
- Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
- Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
- Perron, Pierre, 1991.
"A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept,"
Econometric Society, vol. 59(1), pages 211-236, January.
- Perron,P., 1988. "A Continuous Time Approximation To The Unstable First- Order Autoregressive Process: The Case Without An Intercept," Papers 337, Princeton, Department of Economics - Econometric Research Program.
- 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.
- Tom Doan, "undated". "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- 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.
- Lopez, J. Humberto, 1997. "The power of the ADF test," Economics Letters, Elsevier, vol. 57(1), pages 5-10, November.
- 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 1057-1072, June.
- Nabeya, Seiji & Tanaka, Katsuto, 1990. "A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors," Econometrica, Econometric Society, vol. 58(1), pages 145-163, January.
- 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.
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