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Deterministic Seasonality in Dickey-Fuller Tests: Should We Care?

  • Artur C. B. da Silva Lopes


This paper investigates the properties of Dickey-Fuller tests for seasonally unadjusted quarterly data when deterministic seasonality is present but it is neglected in the test regression. While for the random walk case the answer is straightforward, an extensive Monte Carlo study has to be performed for more realistic processes and testing strategies. The most important conclusion is that the common perception that deterministic seasonality has nothing to do with the long-run properties of the data is incorrect. Further numerical evidence on the shortcomings of the general-to-specific t-sig lag selection method is also presented.

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Paper provided by EconWPA in its series Econometrics with number 0402007.

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Length: 22 pages
Date of creation: 14 Feb 2004
Date of revision: 18 Mar 2004
Handle: RePEc:wpa:wuwpem:0402007
Note: Type of Document - pdf; prepared on Win98; pages: 22. version 2.0
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  1. Artur C. B. da Silva Lopes, 2003. "The order of integration for quarterly macroeconomic time series: A simple testing strategy," Empirical Economics, Springer, vol. 28(4), pages 783-794, November.
  2. Nelson, C-R & Murray, C-J, 1997. "The Uncertain Trend in U.S. GDP," Working Papers 97-05, University of Washington, Department of Economics.
  3. Paulo Rodrigues & Denise Osborn, 1999. "Performance of seasonal unit root tests for monthly data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 985-1004.
  4. Abeysinghe, Tilak, 1994. "Deterministic seasonal models and spurious regressions," Journal of Econometrics, Elsevier, vol. 61(2), pages 259-272, April.
  5. Kiviet, Jan F & Phillips, Garry D A, 1992. "Exact Similar Tests for Unit Roots and Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 349-67, August.
  6. Matei Demetrescu & Uwe Hassler, 2007. "Effect of neglected deterministic seasonality on unit root tests," Statistical Papers, Springer, vol. 48(3), pages 385-402, September.
  7. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
  8. Wolters, Jürgen & Hassler, Uwe, 2005. "Unit root testing," Discussion Papers 2005/23, Free University Berlin, School of Business & Economics.
  9. Taylor, A M Robert, 2000. " The Finite Sample Effects of Deterministic Variables on Conventional Methods of Lag-Selection in Unit Root Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(2), pages 293-304, May.
  10. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220 National Bureau of Economic Research, Inc.
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  12. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 277-80, July.
  13. 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.
  14. Pantula, Sastry G, 1991. "Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 63-71, January.
  15. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
  16. Christine Lim & Michael McAleer, 2000. "A seasonal analysis of Asian tourist arrivals to Australia," Applied Economics, Taylor & Francis Journals, vol. 32(4), pages 499-509.
  17. Franses, Philip Hans & Haldrup, Niels, 1994. "The Effects of Additive Outliers on Tests for Unit Roots and Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 471-78, October.
  18. 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.
  19. 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.
  20. Ghysels, Eric, 1990. "Unit-Root Tests and the Statistical Pitfalls of Seasonal Adjustment: The Case of U.S. Postwar Real Gross National Product," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 145-52, April.
  21. Artur C. B. da Silva Lopes, 1999. "Spurious deterministic seasonality and autocorrelation corrections with quarterly data: Further Monte Carlo results," Empirical Economics, Springer, vol. 24(2), pages 341-359.
  22. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  23. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
  24. 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.
  25. repec:cup:cbooks:9780521565882 is not listed on IDEAS
  26. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Universite de Montreal, Departement de sciences economiques.
  27. Kivilcim Metin & Ilker Muslu, 1999. "Money demand, the Cagan model, testing rational expectations vs adaptive expectations: The case of Turkey," Empirical Economics, Springer, vol. 24(3), pages 415-426.
  28. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-70, October.
  29. Perron, P. & Rodriguez, G., 2000. "Seraching for Additive Outliers in Nonstationary Time Series," Working Papers 0005e, University of Ottawa, Department of Economics.
  30. Franses, Philip Hans & Hylleberg, Svend & Lee, Hahn S., 1995. "Spurious deterministic seasonality," Economics Letters, Elsevier, vol. 48(3-4), pages 249-256, June.
  31. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  32. Francisco J. MartÎn-âlvarez & Victor J. Cano-FernÂndez & JosÊ J. CÂceres-HernÂndez, 1999. "The introduction of seasonal unit roots and cointegration to test index aggregation optimality: An application to a Spanish farm price index," Empirical Economics, Springer, vol. 24(3), pages 403-414.
  33. Jeffrey A. Miron, 1996. "The Economics of Seasonal Cycles," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262133237, June.
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