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Deterministic Seasonality versus Seasonal Fractional Integration

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  • Luis A. Gil-Alana

    (School of Economics and Business Administration, University of Navarra)

Abstract

We propose in this article the use of a testing procedure due to Robinson (1994) for testing deterministic seasonality versus seasonal fractional integration. A new statistic, based on the score principle, is developed to simultaneously test both the order of integration of the seasonal component and the need of seasonal dummies. Both tests have standard null and local limit distributions. However, finite-sample critical values of the tests are computed, and experiments based on Monte Carlo show that the sizes of the asymptotic tests are too large, these larger sizes being also associated with some superior rejection frequencies compared with the finite-sample-based tests. Using quarterly data for real consumption and income in Canada, the UK and Japan, the results show that both variables are seasonally fractionally integrated for the three countries without need of deterministic seasonal dummies. We also find evidence that the series may be seasonally fractionally cointegrated.

Suggested Citation

  • Luis A. Gil-Alana, 2004. "Deterministic Seasonality versus Seasonal Fractional Integration," Faculty Working Papers 07/04, School of Economics and Business Administration, University of Navarra.
    • Handle: RePEc:una:unccee:wp0704
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    References listed on IDEAS

    as
    1. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    2. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
    3. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    4. Paramsothy Silvapulle, 2001. "A Score Test For Seasonal Fractional Integration And Cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 85-104.
    5. 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.
    6. L. A. Gil‐Alana, 2001. "Testing Stochastic Cycles in Macroeconomic Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 411-430, July.
    7. Ooms, Marius & Hassler, Uwe, 1997. "On the effect of seasonal adjustment on the log-periodogram regression," Economics Letters, Elsevier, vol. 56(2), pages 135-141, October.
    8. Davidson, James E H, et al, 1978. "Econometric Modelling of the Aggregate Time-Series Relationship between Consumers' Expenditure and Income in the United Kingdom," Economic Journal, Royal Economic Society, vol. 88(352), pages 661-692, December.
    9. Gil-Alana, Luis A., 1999. "Testing fractional integration with monthly data," Economic Modelling, Elsevier, vol. 16(4), pages 613-629, December.
    10. Arteche, Josu & Robinson, Peter M., 1998. "Seasonal and cyclical long memory," LSE Research Online Documents on Economics 2241, London School of Economics and Political Science, LSE Library.
    11. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    12. Carlin, J. B. & Dempster, A. P. & Jonas, A. B., 1985. "On models and methods for Bayesian time series analysis," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 67-90.
    13. Josu Arteche, 2002. "Semiparametric robust tests on seasonal or cyclical long memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 251-285, May.
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    Cited by:

    1. Guglielmo Maria Caporale & Juncal Cunado & Luis A. Gil-Alana, 2007. "Deterministic versus Stochastic Seasonal Fractional Integration and Structural Breaks," CESifo Working Paper Series 1989, CESifo.
    2. Gil-Alana, Luis A. & Fischer, Christian, 2007. "International traveling and trade: further evidence for the case of Spanish wine based on fractional VAR specifications," 105th Seminar, March 8-10, 2007, Bologna, Italy 7859, European Association of Agricultural Economists.

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    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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