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TESTING FOR SEASONAL UNIT ROOTS IN PERIODIC INTEGRATED AUTOREGRESSIVE PROCESSES

Published online by Cambridge University Press:  04 April 2008

Tomas del Barrio Castro  and
Denise R. Osborn
Tomas del Barrio Castro
Affiliation:
University of the Balearic Islands
Denise R. Osborn*
Affiliation:
University of Manchester
*
Address correspondence to Denise R. Osborn, Economics, School of Social Sciences, University of Manchester, Manchester M13 9PL, United Kingdom; e-mail: denise.osborn@manchester.ac.uk.
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Abstract

This paper examines the implications of applying the Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) (HEGY) seasonal root tests to a process that is periodically integrated. As an important special case, the random walk process is also considered, where the zero-frequency unit root t-statistic is shown to converge to the Dickey–Fuller distribution and all seasonal unit root statistics diverge. For periodically integrated processes and a sufficiently high order of augmentation, the HEGY t-statistics for unit roots at the zero and semiannual frequencies both converge to the same Dickey–Fuller distribution. Further, the HEGY joint test statistic for a unit root at the annual frequency and all joint test statistics across frequencies converge to the square of this distribution. Results are also derived for a fixed order of augmentation. Finite-sample Monte Carlo results indicate that, in practice, the zero-frequency HEGY statistic (with augmentation) captures the single unit root of the periodic integrated process, but there may be a high probability of incorrectly concluding that the process is seasonally integrated.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 1093 - 1129
Copyright
Copyright © Cambridge University Press 2008

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