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Periodic Cointegration: Representation and Inference

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  • Boswijk, H Peter
  • Franses, Philip Hans

Abstract

This paper considers a new approach to the analysis of stable relationships between nonstationary seasonal time series. The basis of this approach is an error correction model in which both long-run effects and adjustment parameters are allowed to vary per season. First, we discuss theoretical arguments for such a periodic error correction model. We define periodic cointegration and compare this to the concept of seasonal cointegration. Next, we analyze statistical inference in the periodic error correction model. A sequential procedure is proposed, consisting of a test for periodic cointegration, an estimator of the cointegration parameters and adjustment coefficients, and a class of tests for the hypothesis that some of the parameters are constant over the seasons. The finite sample behavior of the proposed test statistics is analyzed in a limited Monte Carlo exercise. We conclude the paper with an application to a model of aggregate Swedish consumption. Copyright 1995 by MIT Press.

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  • Boswijk, H Peter & Franses, Philip Hans, 1995. "Periodic Cointegration: Representation and Inference," The Review of Economics and Statistics, MIT Press, vol. 77(3), pages 436-454, August.
  • Handle: RePEc:tpr:restat:v:77:y:1995:i:3:p:436-54
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    Cited by:

    1. del Barrio Castro, Tom s & Osborn, Denise R., 2008. "Cointegration For Periodically Integrated Processes," Econometric Theory, Cambridge University Press, pages 109-142.
    2. Tomas del Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2013. "The trade balance in euro countries: a natural case study of periodic integration with a changing mean," Working Papers 1321, Department of Applied Economics II, Universidad de Valencia.
    3. Lof, Marten & Hans Franses, Philip, 2001. "On forecasting cointegrated seasonal time series," International Journal of Forecasting, Elsevier, pages 607-621.
    4. Bohl, Martin T., 2000. "Nonstationary stochastic seasonality and the German M2 money demand function," European Economic Review, Elsevier, vol. 44(1), pages 61-70, January.
    5. Mårten Löf & Johan Lyhagen, 2003. "On seasonal error correction when the processes include different numbers of unit roots," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(5), pages 377-389.
    6. Christiano, Lawrence J. & Todd, Richard M., 2002. "The conventional treatment of seasonality in business cycle analysis: does it create distortions?," Journal of Monetary Economics, Elsevier, pages 335-364.
    7. Tomas Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2015. "An analysis of the trade balance for OECD countries using periodic integration and cointegration," Empirical Economics, Springer, pages 389-402.
    8. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    9. Fantazzini, Dean & Toktamysova, Zhamal, 2015. "Forecasting German car sales using Google data and multivariate models," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 97-135.
    10. Arnade, Carlos & Pick, Daniel, 1998. "Seasonality and unit roots: the demand for fruits," Agricultural Economics, Blackwell, pages 53-62.
    11. Evans, Mark, 2006. "A study of the relationship between regional ferrous scrap prices in the USA, 1958-2004," Resources Policy, Elsevier, vol. 31(2), pages 65-77, June.
    12. Novales, Alfonso & de Fruto, Rafael Flores, 1997. "Forecasting with periodic models A comparison with time invariant coefficient models," International Journal of Forecasting, Elsevier, vol. 13(3), pages 393-405, September.
    13. Dr. Godwin Chukwudum Nwaobi, 2004. "Modelling Economic Fluctuations In Subsaharan Africa:A Vector Autoregressive Approach," Macroeconomics 0406008, EconWPA.
    14. Wells, J. M., 1997. "Modelling seasonal patterns and long-run trends in U.S. time series," International Journal of Forecasting, Elsevier, vol. 13(3), pages 407-420, September.
    15. 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.
    16. Albertson, Kevin & Aylen, Jonathan, 1999. "Forecasting using a periodic transfer function: with an application to the UK price of ferrous scrap," International Journal of Forecasting, Elsevier, vol. 15(4), pages 409-419, October.

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