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Testing for Seasonal Fractional Roots in German Real Output

  • Guglielmo M. Caporale
  • Luis A. Gil-Alana

This paper examines the seasonal structure of German real GNP per capita by using a version of Robinson's (1994) tests which is suitable in the context of seasonality. This method has several advantages over alternative approaches when testing for seasonal unit roots. First, unlike standard tests, which are nested in AR alternatives, it is embedded in fractional alternatives. Second, it allows testing at the zero frequency and at each of the seasonal frequencies separately. Third, it makes it possible to test for different orders of integration at each of the frequencies simultaneously. The empirical analysis suggests that the real output series may have a unit root at the zero frequency, and fractional rather than unit roots at the seasonal ones. This is in contrast to the findings reported by Lutkepohl et al. (1999) in their study on German money demand, and shows the importance of modelling the seasonal features of the data in alternative ways. Copyright Verein für Socialpolitik and Blackwell Publishing Ltd. 2004.

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Article provided by Verein für Socialpolitik in its journal German Economic Review.

Volume (Year): 5 (2004)
Issue (Month): 3 (08)
Pages: 319-333

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Handle: RePEc:bla:germec:v:5:y:2004:i:3:p:319-333
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  1. H. Lütkepohl & T. Teräsvirta & J. Wolters, 1995. "Investigating Stability and Linearity of a German M1 Money Demand Function," SFB 373 Discussion Papers 1995,57, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal Integration And Cointegration," Papers 0-88-2, Pennsylvania State - Department of Economics.
  3. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
  4. Gil-Alana, Luis A., 2001. "A fractionally integrated model with a mean shift for the US and the UK real oil prices," Economic Modelling, Elsevier, vol. 18(4), pages 643-658, December.
  5. Charles S. Bos & Philip Hans Franses & Marius Ooms, 1998. "Long Memory and Level Shifts: Re-Analyzing Inflation Rates," Tinbergen Institute Discussion Papers 98-039/4, Tinbergen Institute.
  6. Gil-Alana, Luis A., 1999. "Testing fractional integration with monthly data," Economic Modelling, Elsevier, vol. 16(4), pages 613-629, December.
  7. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
  8. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  9. Granger, Clive W.J. & Hyung, Namwon, 1999. "Occasional Structural Breaks and Long Memory," University of California at San Diego, Economics Working Paper Series qt4d60t4jh, Department of Economics, UC San Diego.
  10. Hylleberg, Svend & Jorgensen, Clara & Sorensen, Nils Karl, 1993. "Seasonality in Macroeconomic Time Series," Empirical Economics, Springer, vol. 18(2), pages 321-35.
  11. L. A. Gil-Alaña & Peter M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," LSE Research Online Documents on Economics 298, London School of Economics and Political Science, LSE Library.
  12. Hylleberg, Svend, 1995. "Tests for seasonal unit roots general to specific or specific to general?," Journal of Econometrics, Elsevier, vol. 69(1), pages 5-25, September.
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