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Is Seasonal Adjustment a Linear or Nonlinear Data Filtering Process?

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  • Eric Ghysels

    ()

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

Abstract

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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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 95s-19.

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Date of creation: 01 Mar 1995
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Handle: RePEc:cir:cirwor:95s-19

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Keywords: X-11 program; Nonlinearity; X-11 program ; Nonlinearity;

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References

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  1. Cannings, K. & Montmarquette, C. & Mahseredjian, S., 1994. "Major Choice: Undergraduate Concentrations and the Probability of Graduation," Cahiers de recherche 9419, Universite de Montreal, Departement de sciences economiques.
  2. 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.
  3. 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.
  4. 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.
  5. Boyer, M. & Laffont, J.J., 1995. "Environmental Risks and Bank Liability," Cahiers de recherche 9501, Universite de Montreal, Departement de sciences economiques.
  6. Grether, D M & Nerlove, M, 1970. "Some Properties of 'Optimal' Seasonal Adjustment," Econometrica, Econometric Society, vol. 38(5), pages 682-703, September.
  7. Fisher, T.C.G. & Martel, J., 1994. "The Creditors' Financial Reorganization Decision: New Evidence from Canadian Data," Cahiers de recherche 9417, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. 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.
  9. 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.
  10. Ghysels, E. & Perron, P., 1990. "The Effect Of Seasonal Adjustment Filters On Tests For A Unit Root," Papers 355, Princeton, Department of Economics - Econometric Research Program.
  11. 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.
  12. 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.
  13. 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.).
  14. 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.
  15. Ghysels, Eric, 1997. "Seasonal Adjustment and Other Data Transformations," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 410-18, October.
  16. 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.
  17. 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.
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Citations

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Cited by:
  1. Chu, Ching-Wu & Zhang, Guoqiang Peter, 2003. "A comparative study of linear and nonlinear models for aggregate retail sales forecasting," International Journal of Production Economics, Elsevier, vol. 86(3), pages 217-231, December.
  2. Timmermann, Allan G, 2005. "Forecast Combinations," CEPR Discussion Papers 5361, C.E.P.R. Discussion Papers.
  3. Eric Ghysels & Clive W.J. Granger & Pierre L. Siklos, 1997. "Seasonal Adjustment and Volatility Dynamics," CIRANO Working Papers 97s-39, CIRANO.
  4. Lawrence J. Christiano & Richard M. Todd, 2000. "The Conventional Treatment of Seasonality in Business Cycle Analysis: Does it Create Distortions?," NBER Technical Working Papers 0266, National Bureau of Economic Research, Inc.
  5. Cubadda, Gianluca & Omtzigt, Pieter, 2003. "Small Sample Improvements in the Statistical Analysis of Seasonally Cointegrated Systems," Economics & Statistics Discussion Papers esdp03012, University of Molise, Dept. SEGeS.
  6. Gianluca Cubadda, 2001. "Common Features In Time Series With Both Deterministic And Stochastic Seasonality," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 201-216.
  7. Zhang, G. Peter & Qi, Min, 2005. "Neural network forecasting for seasonal and trend time series," European Journal of Operational Research, Elsevier, vol. 160(2), pages 501-514, January.
  8. Martin Sola & Zacharias Psaradakis, 2002. "On Detrending and Cyclical Asymmetry," Department of Economics Working Papers 020, Universidad Torcuato Di Tella.
  9. Franses, Philip Hans & Paap, Richard, 1999. "Does Seasonality Influence the Dating of Business Cycle Turning Points?," Journal of Macroeconomics, Elsevier, vol. 21(1), pages 79-92, January.
  10. A Matas-Mir & D R Osborn, 2003. "Seasonal Adjustment and the Detection of Business Cycle Phases," The School of Economics Discussion Paper Series 0304, Economics, The University of Manchester.
  11. Fok, D. & Franses, Ph.H.B.F. & Paap, R., 2005. "Performance of Seasonal Adjustment Procedures: Simulation and Empirical Results," Econometric Institute Research Papers EI 2005-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  12. Philip Kostov & John Lingard, 2005. "Seasonally specific model analysis of UK cereals prices," Econometrics 0507014, EconWPA.
  13. Lacroix, R., 2008. "Analyse conjoncturelle de données brutes et estimation de cycles Partie 2 : mise en oeuvre empirique," Working papers 210, Banque de France.
  14. James H. Stock & Mark W. Watson, 1998. "A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series," NBER Working Papers 6607, National Bureau of Economic Research, Inc.
  15. Touhami, A. & Martens, A., 1996. "Macroemesures in Computable General Equilibrium Models: a Probabilistic Treatment with an Application to Morocco," Cahiers de recherche 9621, Universite de Montreal, Departement de sciences economiques.
  16. Antonio Matas-Mir & Denise R. Osborn & Marco Lombardi, 2005. "The Effect of Seasonal Adjustment on the Properties of Business Cycle Regimes," Econometrics Working Papers Archive wp2005_15, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".

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