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A Note On Testing For Seasonal Cointegration Using Principal Components In The Frequency Domain

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  • Gianluca Cubadda

Abstract

. This paper deals with testing for cointegration at any frequency with a focus on the bounds tests proposed by Joyeux (Tests for seasonal cointegration using principal components. J. Time Ser. Anal. 13 (1992), 109–18). It is shown that this class of tests has asymptotic size equal to one because the author does not take into account non‐contemporaneous cointegration at frequencies other than zero and π. The consequences of this size distortion with finite samples are investigated by a Monte Carlo experiment. Bounds tests for contemporaneous cointegration are also proposed. Finally, an empirical example of testing for seasonal cointegration in monthly time series is presented and discussed.

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  • Gianluca Cubadda, 1995. "A Note On Testing For Seasonal Cointegration Using Principal Components In The Frequency Domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 499-508, September.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:5:p:499-508
    DOI: 10.1111/j.1467-9892.1995.tb00250.x
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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. Roselyne Joyeux, 1992. "Tests For Seasonal Cointegration Using Principal Components," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(2), pages 109-118, March.
    3. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230.
    4. 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.
    5. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
    6. Engle, R. F. & Granger, C. W. J. & Hallman, J. J., 1989. "Merging short-and long-run forecasts : An application of seasonal cointegration to monthly electricity sales forecasting," Journal of Econometrics, Elsevier, vol. 40(1), pages 45-62, January.
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    1. Cubadda, Gianluca, 1999. "Common Cycles in Seasonal Non-stationary Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 273-291, May-June.
    2. 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.
    3. Darne, Olivier, 2004. "Seasonal cointegration for monthly data," Economics Letters, Elsevier, vol. 82(3), pages 349-356, March.

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