The contribution of this paper is twofold. First we extend the large sample results provided for the augmented Dickey-Fuller test by Said and Dickey (1984) and Chang and Park (2002) to the case of the augmented seasonal unit root tests of Hylleberg et al. (1990) [HEGY], inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, while those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters which derive from the lag parameters characterising the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T^1/2) rate is shown to be sufficient. The second contribution of the paper is to explore the use of data-dependent lag selection methods in the context of the augmented HEGY tests. Information criteria based methods along with sequential rules, such as those of Ng and Perron (1995) and Beaulieu and Miron (1993), are compared.
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Tomás del Barrio Castro, Denise R. Osborn and A. M. Robert Taylor
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