ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS
将增广Dickey-Fuller检验的大样本结果扩展到季节性单位根检验，证明零频率和奈奎斯特频率的t统计量极限分布是渐近自由的，而谐波频率的t统计量依赖于滞后参数。
In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), 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, whereas those of the t -statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing 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.