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On seasonal error correction when the processes include different numbers of unit roots

Author

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  • Mårten Löf

    (National Institute of Economic Research, Stockholm, Sweden)

  • Johan Lyhagen

    (Division of Statistics, Uppsala University, Sweden)

Abstract

We propose a seasonal cointegration model (SECM) for quarterly data which includes variables with different numbers of unit roots and thus needs to be transformed in different ways in order to yield stationarity. A Monte Carlo simulation is carried out to investigate the consequences of specifying a SECM with all variables in annual diffrerences in this situation. The SECM in annual differences is compared to the correctly specified model. Pre-testing for unit roots using two different approaches, and where the models are specified according to the unit root test results, is also considered. The forecast mean squared error criterion and certain parameter estimation results indicate that, in practice, a cointegration model where all variables are transformed with the annual difference filter is more robust than one obtained by pre-testing for a smaller number of unit roots. The second-best choice when the true model is not known and when the aim is to forecast, is an ordinary VAR model also in annual differences. Copyright © 2003 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
  • Handle: RePEc:jof:jforec:v:22:y:2003:i:5:p:377-389
    DOI: 10.1002/for.864
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    References listed on IDEAS

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    1. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    2. 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.
    3. 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.
    4. Clements, Michael P. & Hendry, David F., 1997. "An empirical study of seasonal unit roots in forecasting," International Journal of Forecasting, Elsevier, vol. 13(3), pages 341-355, September.
    5. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    6. 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.
    7. Lof, Marten & Lyhagen, Johan, 2002. "Forecasting performance of seasonal cointegration models," International Journal of Forecasting, Elsevier, vol. 18(1), pages 31-44.
    8. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
    9. 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.
    10. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    11. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    12. 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. Carmine Pappalardo & Gianfranco Piras, 2004. "Vector-Autoregression Approach to Forecast Italian Imports," ISAE Working Papers 42, ISTAT - Italian National Institute of Statistics - (Rome, ITALY).

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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