Alternative stratetgies for ‘augmenting’ the dickey-fuller test: size-robustness in the face of pre-testing

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Abstract
The outcome of the ‘augmented’ Dickey-Fuller test for unit roots can be sensitive to the chosen degree of augmentation in the Dickey-Fuller regression. Researchers use a variety of pre-testing techniques to choose this augmentation level, with commensurate implications for the properties of the test. We consider six broad selection strategies which match or mimic some of the procedures encountered in practice, and focus on the true (as opposed to nominal) size of the test in the face of such pre-testing. On balance, our results favour the strategy incorporated into the SHAZAM package in relatively small samples; and favour determining the augmentation level on the basis of the autocorrelation and partial autocorrelation functions of the residuals of the augmented Dickey-Fuller regression when the sample is larger.