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Cointegration For Periodically Integrated Processes

  • del Barrio Castro, Tom s
  • Osborn, Denise R.

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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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 24 (2008)
Issue (Month): 01 (February)
Pages: 109-142

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Handle: RePEc:cup:etheor:v:24:y:2008:i:01:p:109-142_08
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  1. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
  2. 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.
  3. Richard Paap & Philip Hans Franses, 1999. "On trends and constants in periodic autoregressions," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 271-286.
  4. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  5. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
  6. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
  7. 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.
  8. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  9. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
  10. 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.
  11. 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.
  12. 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.
  13. Birchenhall, C R, et al, 1989. "A Seasonal Model of Consumption," Economic Journal, Royal Economic Society, vol. 99(397), pages 837-43, September.
  14. Franses, Philip Hans, 1993. "A method to select between periodic cointegration and seasonal cointegration," Economics Letters, Elsevier, vol. 41(1), pages 7-10.
  15. Niels Haldrup & Svend Hylleberg & Gabriel Pons & Jaume Rosselló & Andreu Sansó, 2005. "Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data," Economics Working Papers 2005-03, School of Economics and Management, University of Aarhus.
  16. 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.
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