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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
Date of revision:
Handle: RePEc:cir:cirwor:99s-05
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  1. 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.
  2. J. Joseph Beaulieu & Jeffrey A. Miron, 1990. "The Seasonal Cycle in U.S. Manufacturing," NBER Working Papers 3450, National Bureau of Economic Research, Inc.
  3. Ghysels, E., 1990. "On the Economic and Econometrics of Seasonality," Cahiers de recherche 9028, Universite de Montreal, Departement de sciences economiques.
  4. repec:cup:cbooks:9780521477444 is not listed on IDEAS
  5. 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.
  6. 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 503-34, June.
  7. 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.
  8. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
  9. Perron, Pierre, 1989. "The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 5(02), pages 241-255, August.
  10. repec:cup:cbooks:9780521471626 is not listed on IDEAS
  11. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June.
  12. Franses, Philip Hans & Hylleberg, Svend & Lee, Hahn S., 1995. "Spurious deterministic seasonality," Economics Letters, Elsevier, vol. 48(3-4), pages 249-256, June.
  13. 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.
  14. Osborn, Denise R., 1990. "A survey of seasonality in UK macroeconomic variables," International Journal of Forecasting, Elsevier, vol. 6(3), pages 327-336, October.
  15. repec:cup:cbooks:9780521405515 is not listed on IDEAS
  16. 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.
  17. 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," Working Papers 92008, Wilfrid Laurier University, Department of Economics.
  18. Rodrigues, Paulo M.M., 2001. "Near Seasonal Integration," Econometric Theory, Cambridge University Press, vol. 17(01), pages 70-86, February.
  19. Hylleberg, Svend & Jorgensen, Clara & Sorensen, Nils Karl, 1993. "Seasonality in Macroeconomic Time Series," Empirical Economics, Springer, vol. 18(2), pages 321-35.
  20. 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 237-52, July.
  21. 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.
  22. repec:cup:cbooks:9780521477451 is not listed on IDEAS
  23. 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.
  24. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  25. 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.
  26. Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303.
  27. Abeysinghe, Tilak, 1994. "Deterministic seasonal models and spurious regressions," Journal of Econometrics, Elsevier, vol. 61(2), pages 259-272, April.
  28. 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.
  29. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  30. Abeysinghe, Tilak, 1991. "Inappropriate use of seasonal dummies in regression," Economics Letters, Elsevier, vol. 36(2), pages 175-179, June.
  31. 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.
  32. 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.
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