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ASYMPTOTIC DISTRIBUTIONS OF SEASONAL UNIT ROOT TESTS: A UNIFYING APPROACH 

Authors: Denise R. Osborn a; Paulo M. M. Rodrigues b
Affiliations:   a School of Economic Studies, University of Manchester, United Kingdom
b Faculty of Economics, University of Algarve, Faro, Portuga
DOI: 10.1081/ETC-120014350
Publication Frequency: 6 issues per year
Published in: journal Econometric Reviews, Volume 21, Issue 2 January 2002 , pages 221 - 241
Formats available: HTML (English) : PDF (English)
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Abstract

This paper adopts a unified approach to the derivation of the asymptotic distributions of various seasonal unit root tests. The procedures considered are those of Dickey et al. [DHF], Kunst, Hylleberg et al. [HEGY], Osborn et al. [OCSB], Ghysels et al. [GHL] and Franses. This unified approach shows that the asymptotic distributions of all these test statistics are functions of the same vector of Brownian motions. The Kunst test and the overall HEGY F-test are, indeed, equivalent both asymptotically and in finite samples, while the Franses and GHL tests are shown to have equivalent parameterizations. The OCSB and DHF test regressions are viewed as restricted forms of the Kunst-HEGY regressions, and these restrictions may have non-trivial asymptotic implications.
Keywords: Seasonal unit roots; Asymptotic distributions; Unit root tests; Brownian motions; JEL Classification; C12; C22
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