IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/112730.html
   My bibliography  Save this paper

Testing for the cointegration rank between Periodically Integrated processes

Author

Listed:
  • del Barrio Castro, Tomás

Abstract

Cointegration between periodically integrated (PI) processes has been analyzed by many, including Bladen-Hovell, Chui, Osborn, and Smith (1989), Boswijk and Franses (1995), Franses and Paap (2004), Kleibergen and Franses (1999) and del Barrio Castro and Osborn (2008), to name a few. However, there is currently no published method that allows us to determine the cointegration rank between P I processes. The present paper Ölls this gap in the literature with a method for determining the cointegration rank between a set of P I processes based on the idea of pseudo-demodulation, as proposed in the context of seasonal cointegration by del Barrio Castro, Cubadda, and Osborn (2020). Once a pseudodemodulated time series is obtained, the Johansen (1995) procedure can be applied to determine the cointegration rank. A Monte Carlo experiment shows that the proposed approach works satisfactorily for small samples.

Suggested Citation

  • del Barrio Castro, Tomás, 2022. "Testing for the cointegration rank between Periodically Integrated processes," MPRA Paper 112730, University Library of Munich, Germany, revised 2022.
    • Handle: RePEc:pra:mprapa:112730
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/112730/1/MPRA_paper_112730.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/112731/1/MPRA_paper_112728.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Engle, R. F. & Granger, C. W. J. & Hylleberg, S. & Lee, H. S., 1993. "The Japanese consumption function," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 275-298.
    3. 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.
    4. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    5. H. Peter Boswijk & Philip Hans Franses, 1996. "Unit Roots In Periodic Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(3), pages 221-245, May.
    6. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    7. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    8. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    9. 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.
    10. Haldrup, Niels & Hylleberg, Svend & Pons, Gabriel & Sanso, Andreu, 2007. "Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 21-32, January.
    11. Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303.
    12. Richard Paap & Philip Hans Franses, 1999. "On trends and constants in periodic autoregressions," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 271-286.
    13. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-266, October-D.
    14. 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.
    15. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
    16. Kleibergen, F.R. & Franses, Ph.H.B.F., 1999. "Cointegration in a periodic vector autoregression," Econometric Institute Research Papers EI 9906-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. 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.
    18. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
    19. Xiao, Zhijie & Phillips, Peter C.B., 1999. "Efficient Detrending In Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 15(4), pages 519-548, August.
    20. Hansen, Lars Peter & Sargent, Thomas J., 1993. "Seasonality and approximation errors in rational expectations models," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 21-55.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. del Barrio Castro, Tomás, 2021. "Testing for the cointegration rank between Periodically Integrated processes," MPRA Paper 106603, University Library of Munich, Germany, revised 2021.
    2. 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.
    3. 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.
    4. Tomás Barrio & Mariam Camarero & Cecilio Tamarit, 2019. "Testing for Periodic Integration with a Changing Mean," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 45-75, June.
    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. Pami Dua & Lokendra Kumawat, 2005. "Modelling and Forecasting Seasonality in Indian Macroeconomic Time Series," Working papers 136, Centre for Development Economics, Delhi School of Economics.
    7. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    8. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    9. del Barrio Castro Tomás & Osborn Denise R, 2011. "Nonparametric Tests for Periodic Integration," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-35, February.
    10. 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.
    11. 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.
    12. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
    13. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    14. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, September.
    15. 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.
    16. Marco Centoni & Gianluca Cubadda, 2011. "Modelling comovements of economic time series: a selective survey," Statistica, Department of Statistics, University of Bologna, vol. 71(2), pages 267-294.
    17. Franses, Philip Hans & van Dijk, Dick, 2005. "The forecasting performance of various models for seasonality and nonlinearity for quarterly industrial production," International Journal of Forecasting, Elsevier, vol. 21(1), pages 87-102.
    18. Zou, Nan & Politis, Dimitris N., 2021. "Bootstrap seasonal unit root test under periodic variation," Econometrics and Statistics, Elsevier, vol. 19(C), pages 1-21.
    19. Reimers, Hans-Eggert, 1997. "Forecasting of seasonal cointegrated processes," International Journal of Forecasting, Elsevier, vol. 13(3), pages 369-380, September.
    20. Jacek Kotlowski, 2005. "Money and prices in the Polish economy. Seasonal cointegration approach," Working Papers 20, Department of Applied Econometrics, Warsaw School of Economics.

    More about this item

    Keywords

    Reduced Rank Regression; Periodic Cointegration; Periodically Integrated Processes.;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:112730. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.