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Testing For Seasonal Unit Roots In Periodic Integrated Autoregressive Processes

  • Castro, Tomas del Barrio
  • Osborn, Denise R.

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.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 24 (2008)
Issue (Month): 04 (August)
Pages: 1093-1129

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Handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:1093-1129_08
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