The Asymptotic Size and Power of the Augmented Dickey-Fuller Test for a Unit Root
AbstractIt 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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Date of creation: 01 Dec 2013
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Social and Behavioral Sciences; Autoregressive Representation; Hypothesis Testing; Integrated Series; Unit Root;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-02-02 (All new papers)
- NEP-ECM-2014-02-02 (Econometrics)
- NEP-ETS-2014-02-02 (Econometric Time Series)
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