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Likelihood analysis of seasonal cointegration

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  • Johansen, Soren
  • Schaumburg, Ernst

Abstract

The vector autoregressive model for seasonal cointegration is analysed. The general error correction model is discussed and conditions are found under which the process is integrated of order 1 at seasonal frequency and exhibits cointegration. Under these conditions a representation theorem for the solution is given expressed in terms of seasonal random walks. Finally the asymptotic properties of the likelihood ratio test for cointegrating rank is given, and it is shown that the estimated cointegrating vectors are asymptotically mixed Gaussian. The results resemble the result for cointegration at zero frequency but expressed in terms of a complex Brownian motion. Tables are provided for asymptotic inference under various assumptions on the deterministic terms.
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  • Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    • Handle: RePEc:eee:econom:v:88:y:1998:i:2:p:301-339
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    1. 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.
    2. Philip Hans Franses & Robert M. Kunst, 1999. "On the Role of Seasonal Intercepts in Seasonal Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(3), pages 409-433, August.
    3. Engle, R. F. & Granger, C. W. J. (ed.), 1991. "Long-Run Economic Relationships: Readings in Cointegration," OUP Catalogue, Oxford University Press, number 9780198283393.
    4. Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303.
    5. Harbo, Ingrid, et al, 1998. "Asymptotic Inference on Cointegrating Rank in Partial Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 388-399, October.
    6. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
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    • C00 - Mathematical and Quantitative Methods - - General - - - General

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