The authors thank Robert Taylor and a referee for useful comments on an earlier draft of this article. Also, Tomás del Barrio Castro gratefully acknowledges financial support from Ministerio de Educación y Ciencia ECO2008 05215.
HEGY Tests in the Presence of Moving Averages*
Article first published online: 13 APR 2011
© Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2011
Oxford Bulletin of Economics and Statistics
Volume 73, Issue 5, pages 691–704, October 2011
How to Cite
Castro, T. D. B. and Osborn, D. R. (2011), HEGY Tests in the Presence of Moving Averages. Oxford Bulletin of Economics and Statistics, 73: 691–704. doi: 10.1111/j.1468-0084.2011.00633.x
- Issue published online: 14 SEP 2011
- Article first published online: 13 APR 2011
- Final Manuscript Received: October 2010
We analyze the asymptotic distributions associated with the seasonal unit root tests of Hylleberg et al. (1990) for quarterly data when the innovations follow a moving average process. Although both the t- and F-type tests suffer from scale and shift effects compared with the presumed null distributions when a fixed order of autoregressive augmentation is applied, these effects disappear when the order of augmentation is sufficiently large. However, as found by Burridge and Taylor (2001) for the autoregressive case, individual t-ratio tests at the semi-annual frequency are not pivotal even with high orders of augmentation, although the corresponding joint F-type statistic is pivotal. Monte Carlo simulations verify the importance of the order of augmentation for finite samples generated by seasonally integrated moving average processes.