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(Mis)Specification Of Long Memory In Seasonal Time Series

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  • Uwe Hassler

Abstract

. We present a complete generalization of fractional differencing with seasonal processes. The contribution of each seasonal frequency to the variance of a process may be modelled by separate difference parameters. The regression of the log‐periodogram allows estimation of the difference parameters. We approximate the bias and the variance of these estimators with large samples. Numerical examples illustrate the risk of fractional misspecification.

Suggested Citation

  • Uwe Hassler, 1994. "(Mis)Specification Of Long Memory In Seasonal Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(1), pages 19-30, January.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:1:p:19-30
    DOI: 10.1111/j.1467-9892.1994.tb00174.x
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    Citations

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    Cited by:

    1. Laurent Ferrara & Dominique Guegan, 2006. "Fractional seasonality: Models and Application to Economic Activity in the Euro Area," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00185370, HAL.
    2. Guglielmo Maria Caporale & Luis A. Gil‐Alana, 2007. "Nonlinearities and Fractional Integration in the US Unemployment Rate," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(4), pages 521-544, August.
    3. Laurent Ferrara & Dominique Guégan, 2008. "Business surveys modelling with Seasonal-Cyclical Long Memory models," Economics Bulletin, AccessEcon, vol. 3(29), pages 1-10.
    4. Guglielmo Caporale & Luis Gil-Alana, 2008. "Testing for unit and fractional orders of integration in the trend and seasonal components of US monetary aggregates," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 35(3), pages 241-253, July.
    5. 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.
    6. Martin, Gael M. & Nadarajah, K. & Poskitt, D.S., 2020. "Issues in the estimation of mis-specified models of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 215(2), pages 559-573.
    7. Lovcha, Yuliya & Perez-Laborda, Alejandro, 2015. "The Hours Worked–Productivity Puzzle: Identification In A Fractional Integration Setting," Macroeconomic Dynamics, Cambridge University Press, vol. 19(7), pages 1593-1621, October.
    8. José Manuel Belbute & Alfredo Marvão Pereira, 2016. "Does final energy demand in Portugal exhibit long memory? A fractional integration analysis," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 15(2), pages 59-77, August.
    9. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    10. Ben Nasr, Adnen & Trabelsi, Abdelwahed, 2005. "Seasonal and Periodic Long Memory Models in the In�ation Rates," MPRA Paper 22690, University Library of Munich, Germany, revised 03 Feb 2006.
    11. 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.
    12. Proietti, Tommaso & Maddanu, Federico, 2024. "Modelling cycles in climate series: The fractional sinusoidal waveform process," Journal of Econometrics, Elsevier, vol. 239(1).
    13. Caporale Guglielmo M. & Gil-Alana Luis A., 2004. "Testing for Seasonal Fractional Roots in German Real Output," German Economic Review, De Gruyter, vol. 5(3), pages 319-333, August.
    14. José Manuel Madeira Belbute, 2015. "Does Final Energy Demand in Portugal Exhibit Long Memory? A Fractional Integration Analysis," CEFAGE-UE Working Papers 2015_04, University of Evora, CEFAGE-UE (Portugal).
    15. López-García, M.N. & Trinidad-Segovia, J.E. & Sánchez-Granero, M.A. & Pouchkarev, I., 2021. "Extending the Fama and French model with a long term memory factor," European Journal of Operational Research, Elsevier, vol. 291(2), pages 421-426.
    16. repec:ebl:ecbull:v:3:y:2008:i:29:p:1-10 is not listed on IDEAS
    17. Wilfredo Palma & Ngai Hang Chan, 2005. "Efficient Estimation of Seasonal Long‐Range‐Dependent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 863-892, November.
    18. Gil-Alana, Luis A., 2003. "Generalized Fractional Time Series Modelling of the Relationship between Consumption and Income in the UK," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 3(1).
    19. J. Cunado & L.A. Gil-Alana & F. Péarez de Gracia, 2005. "The Nature of Seasonality in Spanish Tourism Time Series," Tourism Economics, , vol. 11(4), pages 483-499, December.

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