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Do Long-Memory Models Have Long Memory?


  • Andersson, Michael K.

    (Dept. of Economic Statistics, Stockholm School of Economics)


This paper examines the predictability memory of fractionally integrated ARMA processes. Very long memory is found for positively fractionally integrated processes with large positive AR parameters. However, negative AR parameters absorb, to a great extent, the memory generated by a positive fractional difference. An MA parameter may also reduce the predictability memory substantially, even if the parameter alone provides hardly any memory.

Suggested Citation

  • Andersson, Michael K., 1998. "Do Long-Memory Models Have Long Memory?," SSE/EFI Working Paper Series in Economics and Finance 227, Stockholm School of Economics, revised 16 Mar 2000.
  • Handle: RePEc:hhs:hastef:0227

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    References listed on IDEAS

    1. George S. Tavlas, 1993. "The ‘New’ Theory of Optimum Currency Areas," The World Economy, Wiley Blackwell, vol. 16(6), pages 663-685, November.
    2. Fleming, J Marcus, 1971. "On Exchange Rate Unification," Economic Journal, Royal Economic Society, vol. 81(323), pages 467-488, September.
    3. U. Michael Bergman & Michael M. Hutchison & Yin-Wong Cheung, "undated". "Should the Nordic Countries Join A European Monetary Union? An Empirical Analysis," EPRU Working Paper Series 97-21, Economic Policy Research Unit (EPRU), University of Copenhagen. Department of Economics.
    4. Benjamin J. Cohen, 1993. "Beyond Emu: The Problem Of Sustainability," Economics and Politics, Wiley Blackwell, vol. 5(2), pages 187-203, July.
    5. Frankel, Jeffrey A. & Rose, Andrew K., 1997. "Is EMU more justifiable ex post than ex ante?," European Economic Review, Elsevier, vol. 41(3-5), pages 753-760, April.
    6. Agathe Cote, "undated". "Exchange Rate Volatility and Trade: A Survey," Staff Working Papers 94-5, Bank of Canada.
    7. Lundborg, Per, 1991. " Determinants of Migration in the Nordic Labor Market," Scandinavian Journal of Economics, Wiley Blackwell, vol. 93(3), pages 363-375.
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    Cited by:

    1. Bengt Assarsson & Pär Österholm, 2015. "Do Swedish Consumer Confidence Indicators Do What They Are Intended to Do?," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot GmbH, Berlin, vol. 61(4), pages 391-404.
    2. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    3. Souza, Leonardo R. & Smith, Jeremy, 2002. "Bias in the memory parameter for different sampling rates," International Journal of Forecasting, Elsevier, vol. 18(2), pages 299-313.
    4. Maria Billstam & Kristina Frändén & Johan Samuelsson & Pär Österholm, 2017. "Quasi-Real-Time Data of the Economic Tendency Survey," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 13(1), pages 105-138, May.
    5. Jan G. De Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Monash Econometrics and Business Statistics Working Papers 12/05, Monash University, Department of Econometrics and Business Statistics.
    6. Man, K. S., 2003. "Long memory time series and short term forecasts," International Journal of Forecasting, Elsevier, vol. 19(3), pages 477-491.
    7. Leonardo Souza & Jeremy Smith & Reinaldo Souza, 2006. "Convex combinations of long memory estimates from different sampling rates," Computational Statistics, Springer, vol. 21(3), pages 399-413, December.
    8. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    9. Andersson, Michael K. & Karlsson, Gustav & Svensson, Josef, 2007. "The Riksbank’s Forecasting Performance," Working Paper Series 218, Sveriges Riksbank (Central Bank of Sweden).

    More about this item


    ARMA; Fractional integration; Prediction horizon;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods


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