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THE IMPACT OF PERSISTENT CYCLES ON ZERO FREQUENCY UNIT ROOT TESTS

Published online by Cambridge University Press:  20 August 2013

Tomás del Barrio Castro ,
Paulo M.M. Rodrigues  and
A.M. Robert Taylor
Tomás del Barrio Castro*
Affiliation:
University of the Balearic Islands
Paulo M.M. Rodrigues*
Affiliation:
Banco de Portugal Universidade Nova de Lisboa and CEFAGE
A.M. Robert Taylor*
Affiliation:
University of Essex
*
*Address correspondence to Robert Taylor, Essex Business School, University of Essex, Colchester CO4 3SQ, United Kingdom, e-mail: rtaylor@essex.ac.uk.
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Abstract

In this paper we investigate the impact of persistent (nonstationary or near nonstationary) cycles on the asymptotic and finite-sample properties of standard unit root tests. Results are presented for the augmented Dickey–Fuller (ADF) normalized bias and t-ratio-based tests (Dickey and Fuller, 1979, Journal of the American Statistical Association 745, 427–431; Said and Dickey, 1984; Biometrika 71, 599–607). the variance ratio unit root test of Breitung (2002, Journal of Econometrics 108, 343–363), and the M class of unit-root tests introduced by Stock (1999, in Engle and White (eds.), A Festschrift in Honour of Clive W.J. Granger) and Perron and Ng (1996, Review of Economic Studies 63, 435–463). We show that although the ADF statistics remain asymptotically pivotal (provided the test regression is properly augmented) in the presence of persistent cycles, this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994, Journal of Business & Economic Statistics 17, 461–470; Ng and Perron, 1995, Journal of the American Statistical Association 90, 268–281) used to determine the order of augmentation in the ADF regression remain valid in the presence of persistent cycles.

Type
MISCELLANEA
Information
Econometric Theory , Volume 29 , Issue 6 , December 2013 , pp. 1289 - 1313
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

We thank the editor, Peter Phillips, the co-editor, Pentti Saikkonen, two anonymous referees, and Bent Nielsen for their helpful and constructive comments on earlier versions of this paper. Tomás del Barrio Castro and Paulo Rodrigues gratefully acknowledge financial support from the Ministerio de Educación y Ciencia ECO2011-23934 and the Fundação para a Ciência e a Tecnologia (POCTI program), respectively.

References

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