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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, Tomás & Osborn, Denise R., 2008. "Cointegration For Periodically Integrated Processes," Econometric Theory, Cambridge University Press, vol. 24(1), pages 109-142, February.
    2. Lof, Marten & Hans Franses, Philip, 2001. "On forecasting cointegrated seasonal time series," International Journal of Forecasting, Elsevier, vol. 17(4), pages 607-621.
    3. 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.
    4. del Barrio Castro, Tomás, 2021. "Testing for the cointegration rank between Periodically Integrated processes," MPRA Paper 106603, University Library of Munich, Germany, revised 2021.
    5. Herwartz, Helmut, 1997. "Performance of periodic error correction models in forecasting consumption data," International Journal of Forecasting, Elsevier, vol. 13(3), pages 421-431, September.
    6. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    7. 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.
    8. 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.
    9. Ripamonti, Alexandre, 2013. "Rational Valuation Formula (RVF) and Time Variability in Asset Rates of Return," MPRA Paper 79460, University Library of Munich, Germany.
    10. Younes Ben Zaied & Marie Estelle Binet, 2015. "Modelling seasonality in residential water demand: the case of Tunisia," Applied Economics, Taylor & Francis Journals, vol. 47(19), pages 1983-1996, April.
    11. Dr. Godwin Chukwudum Nwaobi, 2004. "Modelling Economic Fluctuations In Subsaharan Africa:A Vector Autoregressive Approach," Macroeconomics 0406008, University Library of Munich, Germany.
    12. 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.
    13. 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.
    14. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    15. 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.
    16. 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.
    17. 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, vol. 49(2), pages 335-364, March.
    18. 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, vol. 49(2), pages 389-402, September.
    19. 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.
    20. del Barrio Castro, Tomás, 2021. "Testing for the cointegration rank between Periodically Integrated processes," MPRA Paper 106603, University Library of Munich, Germany, revised 2021.
    21. 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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