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Cointegration for Periodically Integrated Processes

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  • Tomas del Barrio Castro
  • Denise R Osborn

Abstract

Integration for seasonal time series can take the form of seasonal periodic or nonperiodic integration. When seasonal time series are periodically integrated, we show that any cointegration is either full periodic cointegration or full nonperiodic cointegration, with no possibility of cointegration applying for only some seasons. In contrast, seasonally integrated series can be seasonally, periodically or nonperiodically cointegrated, with the possibility of cointegration applying for a subset of seasons. Cointegration tests are analyzed for periodically integrated series. A residual-based test is examined, and its asymptotic distribution is derived under the null hypothesis of no cointegration. A Monte Carlo analysis shows good performance in terms of size and power. The role of deterministic terms in the cointegrating test regression is also investigated. Further, we show that the asymptotic distribution of the error-correction test for periodic cointegration derived by Boswijk and Franses (1995, Review of Economics and Statistics 77, 436 454) does not apply for periodically integrated processes.The authors gratefully acknowledge the comments of participants at the conference on Unit Root and Cointegration Testing, University of the Algave, September October 2005, and they particularly thank two anonymous referees and Helmut L tkepohl (co-editor of this issue of Econometric Theory) for their constructive comments, which have substantially improved the generality of the results in the paper. Tom s del Barrio Castro acknowledges financial support from Ministerio de Educaci n y Ciencia SEJ2005-07781 ECON.

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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 0522.

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Date of creation: 2005
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Handle: RePEc:man:sespap:0522

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  1. Franses, Philip Hans, 1993. "A method to select between periodic cointegration and seasonal cointegration," Economics Letters, Elsevier, vol. 41(1), pages 7-10.
  2. Cubadda, Gianluca, 2001. " Complex Reduced Rank Models for Seasonally Cointegrated Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(4), pages 497-511, September.
  3. Haldrup, Niels & Hylleberg, Svend & Pons, Gabriel & Sanso, Andreu, 2007. "Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 21-32, January.
  4. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, November.
  5. Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal Integration And Cointegration," Papers 0-88-2, Pennsylvania State - Department of Economics.
  6. Peter Boswijk, H., 1994. "Testing for an unstable root in conditional and structural error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 37-60, July.
  7. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  8. 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.
  9. Boswijk, H Peter & Franses, Philip Hans, 1995. "Periodic Cointegration: Representation and Inference," The Review of Economics and Statistics, MIT Press, vol. 77(3), pages 436-54, August.
  10. Johansen, S. & Schaumburg, E., 1997. "Likelihood Analysis of Seasonal Cointegration," Economics Working Papers eco97/16, European University Institute.
  11. Birchenhall, C R, et al, 1989. "A Seasonal Model of Consumption," Economic Journal, Royal Economic Society, vol. 99(397), pages 837-43, September.
  12. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
  13. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June.
  14. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
  15. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
  16. Richard Paap & Philip Hans Franses, 1999. "On trends and constants in periodic autoregressions," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 271-286.
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Cited by:
  1. David R. Bell & Ronald C. Griffin, 2011. "Urban Water Demand with Periodic Error Correction," Land Economics, University of Wisconsin Press, vol. 87(3), pages 528-544.

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