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Is Seasonal Adjustment a Linear or Nonlinear Data Filtering Process?

  • Eric Ghysels
  • Clive W.J. Granger
  • Pierre L. Siklos

In this paper, we investigate whether seasonal adjustment procedures are, at least approximately, linear data transformations. This question is important with respect to many issues including estimation of regression models with seasonally adjusted data. We focus on the X-11 program and first review the features of the program that might be potential sources of nonlinearity. We rely on simulation evidence, involving linear unobserved component ARIMA models, to assess the adequacy of the linear approximation. We define a set of properties for the adequacy of a linear approximation to a seasonal adjustment filter. These properties are examined through statistical tests. Next, we study the effect of X-11 seasonal adjustment on regression statistics assessing the statistical significance of the relationship between economic variables in the same spirit as Sims (1974) and Wallis (1974). These findings are complemented with several empirical examples involving economic data. Nous examinons si la procédure d'ajustement X-11 est approximativement linéaire. Il y a potentiellement plusieurs sources de non-linéarité dans cette procédure. Le but de l'étude est de savoir si ces sources sont effectivement assez importantes pour affecter, par exemple, des résultats d'estimation dans des modèles de régression linéaire. La seule façon de répondre à cette question est par estimation. Nous proposons plusieurs critères qu'on peut utiliser pour juger si une procédure d'ajustement est approximativement linéaire. Nous examinons également par simulation des propriétés de tests dans le modèle de régression dans le même esprit que Sims (1974) et Wallis (1974).

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File URL: http://www.cirano.qc.ca/files/publications/95s-19.pdf
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Paper provided by CIRANO in its series CIRANO Working Papers with number 95s-19.

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Length: 34 pages
Date of creation: 01 Mar 1995
Date of revision:
Handle: RePEc:cir:cirwor:95s-19
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  1. Timothy C. G. Fisher & Jocelyn Martel, 1994. "The Creditors' Financial Reorganization Decision: New Evidence from Canadian Data," CIRANO Working Papers 94s-21, CIRANO.
  2. David M. Grether & Marc Nerlove, 1968. "Some Properties of 'Optimal' Seasonal Adjustment," Cowles Foundation Discussion Papers 261, Cowles Foundation for Research in Economics, Yale University.
  3. Vogelsang, T.J. & Perron, P., 1994. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," Cahiers de recherche 9422, Universite de Montreal, Departement de sciences economiques.
  4. Maravall, Agustin, 1988. "A note on minimum mean squared error estimation of signals with unit roots," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 589-593.
  5. Neil R. Ericsson & David F. Hendry & Hong-Anh Tran, 1993. "Cointegration, seasonality, encompassing, and the demand for money in the United Kingdom," International Finance Discussion Papers 457, Board of Governors of the Federal Reserve System (U.S.).
  6. Marcel Boyer & Jean-Jacques Laffont, 1994. "Environmental Risks and Bank Liability," CIRANO Working Papers 94s-22, CIRANO.
  7. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
  8. Ghysels, Eric & Perron, Pierre, 1993. "The effect of seasonal adjustment filters on tests for a unit root," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 57-98.
  9. Kathy Cannings & Sophie Mahseredjian & Claude Montmarquette, 1994. "Major Choices : Undergraduate Concentrations and the Probability of Graduation," CIRANO Working Papers 94s-09, CIRANO.
  10. Burridge, Peter & Wallis, Kenneth F, 1984. "Unobserved-Components Models for Seasonal Adjustment Filters," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 350-59, October.
  11. Sargent, Thomas J, 1989. "Two Models of Measurements and the Investment Accelerator," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 251-87, April.
  12. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
  13. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  14. Ghysels, Eric, 1997. "Seasonal Adjustment and Other Data Transformations," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 410-18, October.
  15. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
  16. Ghysels, E. & Lieberman, O., 1993. "Dynamic Regression and Filtered Data Series: A Laplace Approximation to the Effects of Filtering in Small Samples," Cahiers de recherche 9335, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  17. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
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