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Autoregression-Based Estimators for ARFIMA Models

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Author Info
John Galbraith ()
Victoria Zinde-Walsh

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Abstract

This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA (p,d,q) models, based on autoregressive approximation. We demonstrate consistency of the estimator for -1/2 < d < 1, and in the stationary case we provide a Normal approximation to the finite-sample distribution which can be used for inference. The method provides good finite-sample performance, comparable with that of ML, and stable performance across a range of stationary and non-stationary values of the fractional differencing parameter. In addition, it appears to be relatively robust to mis-specification of the ARFIMA model to be estimated, and is computationally straightforward.

Nous décrivons une méthode d'estimation pour les paramètres des modèles ARFIMA stationnaires ou non-stationnaires, basée sur l'approximation auto-régressive. Nous démontrons que la procédure est consistante pour -1/2 < d < 1, et dans le cas stationnaire nous donnons une approximation Normale utilisable pour inférence statistique. La méthode fonctionne bien en échantillon fini, et donne des résultats comparables pour la plupart des valeurs du paramètre d, stationnaires ou non. Il y a aussi des indications de robustesse à la mauvaise spécification du modèle ARFIMA à estimer, et le calcul des estimations est simple.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2001s-11.

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Date of creation: 01 Feb 2001
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Handle: RePEc:cir:cirwor:2001s-11

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Related research
Keywords: ARFIMA model; autoregression; fractional integration; long memory; Modèle ARFIMA; autorégression; intégration fractionnelle; mémoire longue;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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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. [Downloadable!] (restricted)
  2. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September. [Downloadable!] (restricted)
    Other versions:
  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
    Other versions:
  4. Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Modified Local Whittle Estimation of the Memory Parameter in the Nonstationary Case," Cowles Foundation Discussion Papers 1265, Cowles Foundation, Yale University. [Downloadable!]
  5. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
  6. Chung, Ching-Fan, 1994. "A note on calculating the autocovariances of the fractionally integrated ARMA models," Economics Letters, Elsevier, vol. 45(3), pages 293-297. [Downloadable!] (restricted)
  7. Tieslau, Margie A. & Schmidt, Peter & Baillie, Richard T., 1996. "A minimum distance estimator for long-memory processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 249-264. [Downloadable!] (restricted)
  8. Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June. [Downloadable!] (restricted)
    Other versions:
  9. Martin, Vance L. & Wilkins, Nigel P., 1999. "Indirect estimation of ARFIMA and VARFIMA models," Journal of Econometrics, Elsevier, vol. 93(1), pages 149-175, November. [Downloadable!] (restricted)
    Other versions:
  10. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October. [Downloadable!] (restricted)
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