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Limiting distribution of the least squaresestimates in polynomial regression with longmemory noises

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  • Mohamed Boutahar

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

Abstract

We give the limiting distribution of the least squares estimator in the polynomial regression model driven by some long memory processes. We prove that with an appropriate normalization, the estimation error converges, in distribution, to a random vector which components are a mixture of stochastic integrals. These integrals are with respect to a Lebesgue measure, and can be computed recursively where the seed is a random variable which depends on the assumptions made on the noise process. The limiting distribution can be Gaussian or non Gaussian.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00409571.

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Date of creation: 01 Jan 2006
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Handle: RePEc:hal:wpaper:halshs-00409571

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Related research

Keywords: Fractional Brownian motion ; Long memory ; Multiple Wiener-Itô integral ; Polynomial regression ; Stochastic integral;

References

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  1. Marmol, Francesc & Velasco, Carlos, 2002. "Trend stationarity versus long-range dependence in time series analysis," Journal of Econometrics, Elsevier, vol. 108(1), pages 25-42, May.
  2. Davidson, James & de Jong, Robert M., 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii," Econometric Theory, Cambridge University Press, vol. 16(05), pages 643-666, October.
  3. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  4. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
  5. 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.
  6. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
  7. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
  8. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
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