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Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models

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  • Doornik, Jurgen A.
  • Ooms, Marius

Abstract

We discuss computational aspects of likelihood-based estimation of univariate ARFIMA (p,d,q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.
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Suggested Citation

  • Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.
    • Handle: RePEc:eee:csdana:v:42:y:2003:i:3:p:333-348
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    References listed on IDEAS

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    1. Smith, Anthony A, Jr & Sowell, Fallaw & Zin, Stanley E, 1997. "Fractional Integration with Drift: Estimation in Small Samples," Empirical Economics, Springer, vol. 22(1), pages 103-116.
    2. Beveridge, Steve & Oickle, Cyril, 1993. "Estimating fractionally integrated time series models," Economics Letters, Elsevier, vol. 43(2), pages 137-142.
    3. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    4. Offer Lieberman, 2001. "Penalised Maximum Likelihood Estimation for Fractional Guassian Processes," Cowles Foundation Discussion Papers 1348, Cowles Foundation for Research in Economics, Yale University.
    5. 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.
    6. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August.
    7. Bollerslev, Tim & Jubinski, Dan, 1999. "Equity Trading Volume and Volatility: Latent Information Arrivals and Common Long-Run Dependencies," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 9-21, January.
    8. 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.
    9. Ooms, M. & Doornik, J.A., 1999. "Inference and Forecasting for Fractional Autoregressive Integrated Moving Average Models, with an application to US and UK inflation," Econometric Institute Research Papers EI 9947/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    1. Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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