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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

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
    4. 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.
    5. Katayama, Naoya, 2007. "Seasonally and Fractionally Differenced Time Series," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 48(1), pages 25-55, June.
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    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.

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