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On the Role of Seasonal Intercepts in Seasonal Cointegration

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  • Philip Hans Franses
  • Robert M. Kunst

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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  • Philip Hans Franses & Robert M. Kunst, 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:409-433
    DOI: 10.1111/1468-0084.00136
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    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. Agnieszka Tłuczak, 2022. "Convergence of prices on the pig market in selected European Union countries. Case study," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 68(3), pages 107-115.
    3. 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.
    4. 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.
    5. Lof, Marten & Hans Franses, Philip, 2001. "On forecasting cointegrated seasonal time series," International Journal of Forecasting, Elsevier, vol. 17(4), pages 607-621.
    6. 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.
    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. Seong, Byeongchan, 2009. "Bonferroni correction for seasonal cointegrating ranks," Economics Letters, Elsevier, vol. 103(1), pages 42-44, April.
    11. Jacek Kotlowski, 2005. "Money and prices in the Polish economy. Seasonal cointegration approach," Working Papers 20, Department of Applied Econometrics, Warsaw School of Economics.
    12. Kunst, Robert M., 1997. "Decision Bounds for Data-Admissible Seasonal Models," Economics Series 51, Institute for Advanced Studies.
    13. Darne, Olivier, 2004. "Seasonal cointegration for monthly data," Economics Letters, Elsevier, vol. 82(3), pages 349-356, March.
    14. 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.
    15. Lof, Marten & Lyhagen, Johan, 2002. "Forecasting performance of seasonal cointegration models," International Journal of Forecasting, Elsevier, vol. 18(1), pages 31-44.
    16. Reimers, Hans-Eggert, 1997. "Forecasting of seasonal cointegrated processes," International Journal of Forecasting, Elsevier, vol. 13(3), pages 369-380, September.
    17. 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.
    18. 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.
    19. Justyna Wr'oblewska, 2020. "Bayesian analysis of seasonally cointegrated VAR model," Papers 2012.14820, arXiv.org, revised Apr 2021.
    20. Robert M. Kunst & Michael Reutter, 2000. "Decisions on Seasonal Unit Roots," CESifo Working Paper Series 286, CESifo.
    21. 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.
    22. Kunst, Robert M., 2009. "A Nonparametric Test for Seasonal Unit Roots," Economics Series 233, Institute for Advanced Studies.
    23. 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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    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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