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On the Role of Seasonal Intercepts in Seasonal Cointegration

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  • Franses, Philip Hans
  • Kunst, Robert M

Abstract

In the paper we consider the role of seasonal intercepts in seasonal cointegration analysis. For the nonseasonal unit root, such intercepts can generate a stochastic trend with a drift common to all observations. For the seasonal unit roots, however, we show that unrestricted seasonal intercepts generate trends that are different across the seasons. Since such seasonal trends may not appear in economic data, we propose a modified empirical method to test for seasonal cointegration. We evaluate our method using Monte Carlo simulations and using a four-dimensional data set of Austrian macroeconomic variables.
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  • Franses, Philip Hans & Kunst, Robert M, 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.
  • Handle: RePEc:bla:obuest:v:61:y:1999:i:3:p:409-33
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    References listed on IDEAS

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    1. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    2. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    4. 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.
    5. Kunst, Robert & Neusser, Klaus, 1990. "Cointegration in a Macroeconomic System," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(4), pages 351-365, Oct.-Dec..
    6. Lee, Hahn S. & Siklos, Pierre L., 1995. "A note on the critical values for the maximum likelihood (seasonal) cointegration tests," Economics Letters, Elsevier, vol. 49(2), pages 137-145, August.
    7. Kunst, Robert M, 1993. "Seasonal Cointegration in Macroeconomic Systems: Case Studies for Small and Large European Countries," The Review of Economics and Statistics, MIT Press, vol. 75(2), pages 325-330, May.
    8. Osterwald-Lenum, Michael, 1992. "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 461-472, August.
    9. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
    10. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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    Cited by:

    1. Cubadda, Gianluca & Omtzigt, Pieter, 2005. "Small-sample improvements in the statistical analysis of seasonally cointegrated systems," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 333-348, April.
    2. Franses, Philip Hans & Kunst, Robert M., 2007. "Analyzing a panel of seasonal time series: Does seasonality in industrial production converge across Europe?," Economic Modelling, Elsevier, vol. 24(6), pages 954-968, November.
    3. Robert M. Kunst & Philip Hans Franses, 2011. "Testing for Seasonal Unit Roots in Monthly Panels of Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(4), pages 469-488, August.
    4. Lof, Marten & Hans Franses, Philip, 2001. "On forecasting cointegrated seasonal time series," International Journal of Forecasting, Elsevier, vol. 17(4), pages 607-621.
    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. Lof, Marten & Lyhagen, Johan, 2002. "Forecasting performance of seasonal cointegration models," International Journal of Forecasting, Elsevier, vol. 18(1), pages 31-44.
    7. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    8. Lee, Hahn Shik & Siklos, Pierre L., 1997. "The role of seasonality in economic time series reinterpreting money-output causality in U.S. data," International Journal of Forecasting, Elsevier, vol. 13(3), pages 381-391, September.
    9. Roberto Cellini & Tiziana Cuccia, 2013. "Museum and monument attendance and tourism flow: a time series analysis approach," Applied Economics, Taylor & Francis Journals, vol. 45(24), pages 3473-3482, August.
    10. Reimers, Hans-Eggert, 1997. "Forecasting of seasonal cointegrated processes," International Journal of Forecasting, Elsevier, vol. 13(3), pages 369-380, September.
    11. Ozlem Tasseven, 2009. "Seasonal Co-integration An Extension of the Johansen and Schaumburg Approach with an Exclusion Test," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 56(1), pages 39-53, March.
    12. Helmut Herwartz & Hans-Eggert Reimers, 2003. "Seasonal cointegration analysis for German M3 money demand," Applied Financial Economics, Taylor & Francis Journals, vol. 13(1), pages 71-78.
    13. Seong, Byeongchan, 2009. "Bonferroni correction for seasonal cointegrating ranks," Economics Letters, Elsevier, vol. 103(1), pages 42-44, April.
    14. Jacek Kotlowski, 2005. "Money and prices in the Polish economy. Seasonal cointegration approach," Working Papers 20, Department of Applied Econometrics, Warsaw School of Economics.
    15. Robert M. Kunst & Michael Reutter, 2000. "Decisions on Seasonal Unit Roots," CESifo Working Paper Series 286, CESifo Group Munich.
    16. Kunst, Robert M., 1997. "Decision Bounds for Data-Admissible Seasonal Models," Economics Series 51, Institute for Advanced Studies.
    17. Darne, Olivier, 2004. "Seasonal cointegration for monthly data," Economics Letters, Elsevier, vol. 82(3), pages 349-356, March.
    18. Gil-Alana, L.A., 2008. "Testing of seasonal integration and cointegration with fractionally integrated techniques: An application to the Danish labour demand," Economic Modelling, Elsevier, vol. 25(2), pages 326-339, March.
    19. Kunst, Robert M., 2009. "A Nonparametric Test for Seasonal Unit Roots," Economics Series 233, Institute for Advanced Studies.
    20. Cubadda, Gianluca, 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.
    21. Gianluca Cubadda, 2001. "Common Features In Time Series With Both Deterministic And Stochastic Seasonality," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 201-216.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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