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The overall seasonal integration tests under non-stationary alternatives: A methodological note

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  • Ghassen El Montasser

Abstract

Few authors have studied, either asymptotically or in finite samples, the size and power of seasonal unit root tests when the data generating process [DGP] is a non-stationary alternative aside from the seasonal random walk. In this respect, Ghysels, lee and Noh (1994) conducted a simulation study by considering the alternative of a non-seasonal random walk to analyze the size and power properties of some seasonal unit root tests. Analogously, Taylor (2005) completed this analysis by developing the limit theory of statistics of Dickey and Fuller Hasza [DHF] (1984) when the data are generated by a non-seasonal random walk. del Barrio Castro (2007) extended the set of non-stationary alternatives and established, for each one, the asymptotic theory of the statistics subsumed in the HEGY procedure. In this paper, I show that establishing the limit theory of F-type statistics for seasonal unit roots can be debatable in such alternatives. The problem lies in the nature of the regressors that these overall F-type tests specify.

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Paper provided by Economics and Econometrics Research Institute (EERI), Brussels in its series EERI Research Paper Series with number EERI_RP_2011_06.

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Date of creation: 06 Apr 2011
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Handle: RePEc:eei:rpaper:eeri_rp_2011_06

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Keywords: Fisher test; seasonal integration; non-stationary alternatives; Brownian motion; Monte Carlo Simulation.;

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  1. 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.
  2. 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.
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