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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- 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.
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- 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.
- 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. Full references (including those not matched with items on IDEAS)
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