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ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

Published online by Cambridge University Press:  27 April 2012

Tomás del Barrio Castro ,
Denise R. Osborn  and
A.M. Robert Taylor
Tomás del Barrio Castro
Affiliation:
University of the Balearic Islands
Denise R. Osborn
Affiliation:
University of Manchester
A.M. Robert Taylor*
Affiliation:
University of Nottingham
*
*Address correspondence to A.M. Robert Taylor, School of Economics, University of Nottingham NG7 2RD, United Kingdom; e-mail: Robert.Taylor@nottingham.ac.uk.
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Abstract

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(T1/2) rate is shown to be sufficient.

Type
Miscellanea
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 1121 - 1143
Copyright
Copyright © Cambridge University Press 2012

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