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Seasonal Unit Root Tests Under Structural Breaks

  • Uwe Hassler
  • Paulo M. M. Rodrigues

In this paper, several seasonal unit root tests are analysed in the context of structural breaks at known time and a new break corrected test is suggested. We show that the widely used HEGY test, as well as an LM variant thereof, are asymptotically robust to seasonal mean shifts of finite magnitude. In finite samples, however, experiments reveal that such tests suffer from severe size distortions and power reductions when breaks are present. Hence, a new break corrected LM test is proposed to overcome this problem. Importantly, the correction for seasonal mean shifts bears no consequence on the limiting distributions, thereby maintaining the legitimacy of canonical critical values. Moreover, although this test assumes a breakpoint a priori, it is robust in terms of misspecification of the time of the break. This asymptotic property is well reproduced in finite samples. Based on a Monte-Carlo study, our new test is compared with other procedures suggested in the literature and shown to hold superior finite sample properties. Copyright 2004 Blackwell Publishing Ltd.

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Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 25 (2004)
Issue (Month): 1 (01)
Pages: 33-53

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Handle: RePEc:bla:jtsera:v:25:y:2004:i:1:p:33-53
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  1. Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers 99-15, Department of Economics, University of Birmingham.
  2. Osborn, Denise R, et al, 1988. "Seasonality and the Order of Integration for Consumption," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(4), pages 361-77, November.
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  6. Paulo M. M. Rodrigues, 2002. "On LM type tests for seasonal unit roots in quarterly data," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 176-195, June.
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  15. Franses, Ph.H.B.F. & Hoek, H. & Paap, R., 1995. "Bayesian Analysis of Seasonal Unit Roots and Seasonal Mean Shifts," Econometric Institute Research Papers EI 9527-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  16. Balcombe, Kelvin, 1999. " Seasonal Unit Root Tests with Structural Breaks in Deterministic Seasonality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 569-82, November.
  17. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-20, July.
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