, Volume 31, Issue 4, pp 333–344 | Cite as

Testing of Unit Root Cycles in the Swedish Economy

  • Luis A. Gil-alana


In this article we examine the existence of unit root cycles in 11 long Swedish macroeconomic time series. We use a version of the tests of Robinson (1994) that permits us to test this type of hypothesis, which is based on the Gegenbauer processes. The results show that, for most of the series, the unit root cycles occur approximately every six periods. However, in case of the GDP deflator and wage rates, first differences may be required before proceeding to the analysis of the cyclical structure.


Long memory unit root cycles macroeconomic time series 


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  1. Ahtola, J., Tiao, G. C. 1987a‘Distributions of least squares estimators of autoregressive parameters for a process with complex roots on the unit circle’Journal of Time Series Analysis8114Google Scholar
  2. Ahtola, J., Tiao, G. C. 1987b‘A note on asymptotic inference in autoregressive models with roots on the unit circle’Journal of Time Series Analysis81518Google Scholar
  3. Arteche, J. 2002‘Semiparametric robust tests on seasonal and cyclical long memory series’Journal of Time Series Analysis23135Google Scholar
  4. Arteche, J., Robinson, P. M. 2000‘Semiparametric inference in seasonal and cyclical long memory processes’Journal of Time Series Analysis21125Google Scholar
  5. Beaudry, P., Koop, G. 1993‘Do recessions permanently change output?’Journal of Monetary Economics31149163Google Scholar
  6. Bhargava, A. 1986‘On the theory of testing for unit roots in observed time series’Review of Economic Studies53369384Google Scholar
  7. Bierens, H. J. 2001‘Complex unit roots and business cycles: Are they real?’Econometric Theory17962983Google Scholar
  8. Candelon, B., Gil-Alana, L.A. 2004‘Fractional integration and business cycle characteristics’Empirical Economics19117Google Scholar
  9. Chan, Y. N. H., Wei, C. Z. 1988‘Limiting distribution of least squares estimates of unstable autoregressive processes’Annals of Statistics16367401Google Scholar
  10. Dickey, D. A., Fuller, W.A. 1979‘Distribution of the estimators for autoregressive time series with a unit root’Journal of the American Statistical Association79427431Google Scholar
  11. Diebold, F. X., Rudebusch, G. D. 1991‘On the power of Dickey and Fuller tests against fractional alternatives’Economics Letters35155160Google Scholar
  12. Englund, P., Persson, T., Svensson, L. E. O. 1992‘Swedish business cycles 1861–1998’Journal of Monetary Economics30343371Google Scholar
  13. Ferrara, L., Guegan, D. 2001‘Forecasting with k-factor Gegenbauer processes: Theory and applications’Journal of Forecasting20581601Google Scholar
  14. Gil-Alana, L. A. 1999‘Testing of fractional integration with monthly data’Economic Modelling16613629Google Scholar
  15. Gil-Alana, L. A. 2001‘Testing of stochastic cycles in macroeconomic time series’Journal of Time Series Analysis22411430Google Scholar
  16. Gil-Alana, L. A., Robinson, P. M. 1997‘Testing of unit roots and other nonstationary hypotheses in macroeconomic time series’Journal of Econometrics80241268Google Scholar
  17. Gil-Alana, L. A., Robinson, P. M. 2001‘Testing of seasonal fractional integration in the UK and Japanese consumption and income’Journal of Applied Econometrics1695114Google Scholar
  18. Gray, H. L., Zhang, N. F., Woodward, W. A. 1989‘On generalized fractional processes’Journal of Time Series Analysis10233257Google Scholar
  19. Gray, H. L., Zhang, N. F., Woodward, W. A. 1994‘On generalized fractional processes.–A correction’Journal of Time Series Analysis15561562Google Scholar
  20. Gregoir, S. 1999‘Efficient tests for the presence of a couple of complex conjugate unit roots in real time series’Santiago de CompostelaSpainPaper Presented at the European Meeting of the Econometric Society 1999Google Scholar
  21. Harvey, A. C. 1985‘Trends and cycles in macroeconomic time series’Journal of Business and Economic Statistics3216227Google Scholar
  22. Hassler, U., Wolters, J. 1994‘On the power of unit root tests against fractional alternatives’Economics Letters4515Google Scholar
  23. Hess, G. D., Iwata, S. 1997‘Measuring and comparing business cycle features’Journal of Business Economics and Statistics15432444Google Scholar
  24. Phillips, P. C. B., Perron, P. 1988‘Testing for a unit root in a time series regression’Biometrika75335346Google Scholar
  25. Perron, P. (1993) ‘Trends, unit roots and structural change in macroeconomic time series’, Unpublished manuscript, University of Montreal, Montreal.Google Scholar
  26. Priestley, M. B. 1981Spectral Analysis and Time SeriesAcademic PressNew YorkGoogle Scholar
  27. Robinson, P. M. 1994‘Efficient tests of non-stationary hypotheses’Journal of the American Statistical Association8914201437Google Scholar
  28. Schmidt, P., Phillips, P. C. B. 1992‘LM tests for a unit root in the presence of deterministic trends’Oxford Bulletin of Economics and Statistics54257287Google Scholar
  29. Skalin, J., Terasvirta, T. 1999‘Another look at Swedish business cycles 1861–1998’Journal of Applied Econometrics14359378Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of NavarrePamplonaSpain

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