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A Score Test for Seasonal Fractional Integration and Cointegration

Author

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  • Param Silvapulle

    (Visitor at The University of Iowa)

Abstract

This paper develops a time domain score statistic for testing fractional integration at zero and seasonal frequencies in quarterly time series models. Further, it introduces the notion of fractional cointegration at different frequencies between two seasonally integrated, I(1) series. In testing problem involving seasonal fractional cointegration, it is argued that the alternative hypothesis is one-sided for which the usual score test may not be appropriate. Therefore, based on the ideas in Silvapulle and Silvapulle (1995), a one-sided score statistics is constructed. A simulation study finds that the score statistic generally has desirable size and power properties in finite samples. The score statistics are applied to the quarterly Australian consumption function. The income and consumption series are found to be I(1) at zero and seasonal frequencies and these two series are not fractionally cointegrated at any frequency.

Suggested Citation

  • Param Silvapulle, 1995. "A Score Test for Seasonal Fractional Integration and Cointegration," Econometrics 9506005, University Library of Munich, Germany, revised 16 Jun 1995.
    • Handle: RePEc:wpa:wuwpem:9506005
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    References listed on IDEAS

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    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. 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.
    3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    5. Christos Agiakloglou & Paul Newbold & Mark Wohar, 1993. "Bias In An Estimator Of The Fractional Difference Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 235-246, May.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    7. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    8. Uwe Hassler, 1993. "Regression Of Spectral Estimators With Fractionally Integrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(4), pages 369-380, July.
    9. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-228, August.
    10. Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303.
    11. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    12. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    Cited by:

    1. Gil-Alaña, Luis A., 2000. "Deterministic seasonality versus seasonal fractional integration," SFB 373 Discussion Papers 2000,106, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Luis A. Gil-Alana, 2003. "Long Memory In Financial Time Series Data With Non-Gaussian Disturbances," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 119-134.
    3. 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.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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