IDEAS home Printed from
   My bibliography  Save this article

Asymptotic prediction of mean squared error for long-memory processes with estimated parameters


  • Naoya Katayama

    (Faculty of Economics, Kyushu University, Fukuoka, Japan)


In this paper we deal with the prediction theory of long-memory time series. The purpose is to derive a general theory of the convergence of moments of the nonlinear least squares estimator so as to evaluate the asymptotic prediction mean squared error (PMSE). The asymptotic PMSE of two predictors is evaluated. The first is defined by the estimator of the differencing parameter, while the second is defined by a fixed differencing parameter: in other words, a parametric predictor of the seasonal autoregressive integrated moving average model. The effects of misspecifying the differencing parameter is a long-memory model are clarified by the asymptotic results relating to the PMSE. The finite sample behaviour of the predictor and the model selection in terms of PMSE of the two predictors are examined using simulation, and the source of any differences in behaviour made clear in terms of asymptotic theory. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Naoya Katayama, 2008. "Asymptotic prediction of mean squared error for long-memory processes with estimated parameters," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 690-720.
  • Handle: RePEc:jof:jforec:v:27:y:2008:i:8:p:690-720 DOI: 10.1002/for.1078

    Download full text from publisher

    File URL:
    File Function: Link to full text; subscription required
    Download Restriction: no

    References listed on IDEAS

    1. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
    2. Tanaka, Katsuto & Maekawa, Koichi, 1984. "The sampling distributions of the predictor for an autoregressive model under misspecifications," Journal of Econometrics, Elsevier, vol. 25(3), pages 327-351, July.
    3. Hidalgo, J. & Yajima, Y., 2002. "Prediction And Signal Extraction Of Strongly Dependent Processes In The Frequency Domain," Econometric Theory, Cambridge University Press, vol. 18(03), pages 584-624, June.
    4. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
    5. Katayama, Naoya, 2007. "Seasonally and Fractionally Differenced Time Series," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 48(1), pages 25-55, June.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Baillie, Richard T. & Kongcharoen, Chaleampong & Kapetanios, George, 2012. "Prediction from ARFIMA models: Comparisons between MLE and semiparametric estimation procedures," International Journal of Forecasting, Elsevier, vol. 28(1), pages 46-53.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jof:jforec:v:27:y:2008:i:8:p:690-720. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.