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Inference of Seasonal Cointegration: Gaussian Reduced Rank Estimation and Tests for Various Types of Cointegration

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  • Sung K. Ahn
  • Sinsup Cho
  • B. Chan Seong

Abstract

An extension of Gaussian reduced rank estimation of Ahn and Reinsel (Journal of Econometrics, Vol. 62, pp. 317–350, 1994) to seasonal periods other than four is presented. Simple adjustments for estimation that are necessary because of complex‐valued seasonal unit roots are presented in detail and the asymptotic distribution of the estimators that takes the same form as that in Ahn and Reinsel (1994) is derived. Tests for contemporaneous cointegration and common polynomial cointegrating vectors (PCIVs) for different seasonal unit roots are presented. Finite sample properties are briefly examined through a small Monte Carlo simulation study and a numerical example is presented to illustrate the methods.

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  • Sung K. Ahn & Sinsup Cho & B. Chan Seong, 2004. "Inference of Seasonal Cointegration: Gaussian Reduced Rank Estimation and Tests for Various Types of Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(2), pages 261-284, May.
  • Handle: RePEc:bla:obuest:v:66:y:2004:i:2:p:261-284
    DOI: 10.1111/j.0305-9049.2003.00100.x
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    References listed on IDEAS

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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. Gregory C. Reinsel & Sung K. Ahn, 1992. "Vector Autoregressive Models With Unit Roots And Reduced Rank Structure:Estimation. Likelihood Ratio Test, And Forecasting," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 353-375, July.
    3. Ahn, Sung K. & Reinsel, Gregory C., 1994. "Estimation of partially nonstationary vector autoregressive models with seasonal behavior," Journal of Econometrics, Elsevier, vol. 62(2), pages 317-350, June.
    4. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
    5. Gianluca Cubadda, 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.
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    Cited by:

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    3. Nyblom, Jukka & Suomala, Jaakko, 2014. "Tests for real and complex unit roots in vector autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 224-239.

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