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HEGY Tests in the Presence of Moving Averages

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  • Tomás Del Barrio Castro
  • Denise R. Osborn

Abstract

We analyze the asymptotic distributions associated with the seasonal unit root tests of the Hylleberg et al. (1990) procedure 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 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.

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File URL: http://hdl.handle.net/10.1111/j.1468-0084.2011.00633.x
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Bibliographic Info

Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics and Statistics.

Volume (Year): 73 (2011)
Issue (Month): 5 (October)
Pages: 691-704

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Handle: RePEc:bla:obuest:v:73:y:2011:i:5:p:691-704

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  1. del Barrio Castro, Tomas, 2006. "On the performance of the DHF tests against nonstationary alternatives," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 291-297, February.
  2. Castro, Tomas del Barrio & Osborn, Denise R., 2008. "Testing For Seasonal Unit Roots In Periodic Integrated Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1093-1129, August.
  3. Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 910-922, November.
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