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Seasonal Nonstationarity and Near-Nonstationarity

  • Eric Ghysels
  • Denise R. Osborn
  • Paulo M. M. Rodrigues

This paper presents a detailed discussion of the characteristics of seasonal integrated and near integrated processes, as well as the asymptotic properties of seasonal unit root tests. More specifically, the characteristics of a seasonal random walk and a more general seasonal integrated ARMA process are analysed. Also the implications of modelling nonstationary stochastic season-ality as deterministic are highlighted. A further observation made includes the asymptotic distributions and power functions of several seasonal unit root tests. Dans cet article, nous étudions les propriétés des processsus avec racines unitaires saisonnières et avec racines quasi-unitaires. Nous traitons le cas des marchés aléatoires ainsi que les processus plus généraux et analysons les distributions des estimateurs et les fonctions de puissances de plusieurs tests.

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File URL: http://www.cirano.qc.ca/files/publications/99s-05.pdf
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Paper provided by CIRANO in its series CIRANO Working Papers with number 99s-05.

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Length: 35 pages
Date of creation: 01 Feb 1999
Handle: RePEc:cir:cirwor:99s-05
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  1. Hylleberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal, Integration And Cointegration," Papers 6-88-2, Pennsylvania State - Department of Economics.
  2. Ghysels, E., 1990. "On The Economic And Econometrics Of Seasonality," Cahiers de recherche 9028, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
  4. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477444, October.
  5. Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303.
  6. 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 361-377, November.
  7. Ghysels, E. & Lee, H.S. & Siklos, P.L., 1992. "On the (Mis)Specification of Seasonality and Its Consequences: An Empirical Investigation With U.S. Data," Cahiers de recherche 9237, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Franses, Philip Hans, 1991. "Seasonality, non-stationarity and the forecasting of monthly time series," International Journal of Forecasting, Elsevier, vol. 7(2), pages 199-208, August.
  9. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
  10. Beaulieu, J. Joseph & Miron, Jeffrey A., 1991. "The seasonal cycle in U.S. manufacturing," Economics Letters, Elsevier, vol. 37(2), pages 115-118, October.
  11. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-1269, September.
  12. J. Joseph Beaulieu & Jeffrey A. Miron, 1992. "Seasonal Unit Roots in Aggregate U.S. Data," NBER Technical Working Papers 0126, National Bureau of Economic Research, Inc.
  13. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
  14. Barsky, Robert B & Miron, Jeffrey A, 1989. "The Seasonal Cycle and the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 503-534, June.
  15. 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.
  16. Denise Osborn & Paulo Rodrigues, 2002. "Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 221-241.
  17. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-252, July.
  18. Rodrigues, Paulo M.M., 2001. "Near Seasonal Integration," Econometric Theory, Cambridge University Press, vol. 17(01), pages 70-86, February.
  19. Franses, Philip Hans & Hylleberg, Svend & Lee, Hahn S., 1995. "Spurious deterministic seasonality," Economics Letters, Elsevier, vol. 48(3-4), pages 249-256, June.
  20. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(03), pages 269-306, September.
  21. Perron, P., 1987. "The Calculation of the Limiting Distribution of the Least Squares Estimator in Near-Integrated Model," Cahiers de recherche 8748, Universite de Montreal, Departement de sciences economiques.
  22. Nabeya, S. & Perron, P., 1991. "Local Asymtotic Distributions Related to the AR(1) MOdel with Dependent Errors," Papers 362, Princeton, Department of Economics - Econometric Research Program.
  23. Engle, R. F. & Granger, C. W. J. & Hylleberg, S. & Lee, H. S., 1993. "The Japanese consumption function," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 275-298.
  24. Abeysinghe, Tilak, 1991. "Inappropriate use of seasonal dummies in regression," Economics Letters, Elsevier, vol. 36(2), pages 175-179, June.
  25. Abeysinghe, Tilak, 1994. "Deterministic seasonal models and spurious regressions," Journal of Econometrics, Elsevier, vol. 61(2), pages 259-272, April.
  26. Rodrigues, Paulo M. M., 2000. "A note on the application of the DF test to seasonal data," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 171-175, April.
  27. Perron, P., 1990. "The Limiting Distribution Of The Least Squares Estimator In Nearly Integrated Seasonal Models," Papers 354, Princeton, Department of Economics - Econometric Research Program.
  28. Osborn, Denise R., 1990. "A survey of seasonality in UK macroeconomic variables," International Journal of Forecasting, Elsevier, vol. 6(3), pages 327-336, October.
  29. Hylleberg, Svend & Jorgensen, Clara & Sorensen, Nils Karl, 1993. "Seasonality in Macroeconomic Time Series," Empirical Economics, Springer, vol. 18(2), pages 321-335.
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