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Estimating and forecasting the long-memory parameter in the presence of periodicity

Author

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  • C. Bisognin

    (Instituto de Matemática-UFRGS, Porto Alegre, Brazil)

  • S. R. C. Lopes

    (Instituto de Matemática-UFRGS, Porto Alegre, Brazil)

Abstract

We consider one parametric and five semiparametric approaches to estimate D in SARFIMA (0, D, 0) s processes, that is, when the process is a fractionally integrated ARMA model with seasonality s. We also consider h-step-ahead forecasting for these processes. We present the proof of some features of this model and also a study based on a Monte Carlo simulation for different sample sizes and different seasonal periods. We compare the different estimation procedures analyzing the bias, the mean squared error values, and the confidence intervals for the estimators. We also consider three different methods to choose the total number of regressors in the regression analysis for the semiparametric class of estimation procedures. We apply the methodology to the Nile River flow monthly data, and also to a simulated seasonal fractionally integrated time series. Copyright © 2007 John Wiley & Sons, Ltd.

Suggested Citation

  • C. Bisognin & S. R. C. Lopes, 2007. "Estimating and forecasting the long-memory parameter in the presence of periodicity," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(6), pages 405-427.
    • Handle: RePEc:jof:jforec:v:26:y:2007:i:6:p:405-427
    DOI: 10.1002/for.1030
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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. Valderio A. Reisen, 1994. "ESTIMATION OF THE FRACTIONAL DIFFERENCE PARAMETER IN THE ARIMA(p, d, q) MODEL USING THE SMOOTHED PERIODOGRAM," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 335-350, May.
    3. Barbara Olbermann & Sílvia Lopes & Valdério Reisen, 2006. "Invariance of the first difference in ARFIMA models," Computational Statistics, Springer, vol. 21(3), pages 445-461, December.
    4. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    5. Ooms, M., 1995. "Flexible Seasonal Long Memory and Economic Time Series," Econometric Institute Research Papers EI 9515-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Clifford M. Hurvich & Bonnie K. Ray, 1995. "Estimation Of The Memory Parameter For Nonstationary Or Noninvertible Fractionally Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 17-41, January.
    7. Ray, Bonnie K., 1993. "Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model," International Journal of Forecasting, Elsevier, vol. 9(2), pages 255-269, August.
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    1. Ye, Xunyu & Gao, Ping & Li, Handong, 2015. "Improving estimation of the fractionally differencing parameter in the SARFIMA model using tapered periodogram," Economic Modelling, Elsevier, vol. 46(C), pages 167-179.

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