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Offline and online weighted least squares estimation of nonstationary power ARCH processes

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  • Aknouche, Abdelhakim
  • Al-Eid, Eid M.
  • Hmeid, Aboubakry M.

Abstract

This paper proposes two estimation methods based on a weighted least squares criterion for non-(strictly) stationary power ARCH models. The weights are the squared volatilities evaluated at a known value in the parameter space. The first method is adapted for fixed sample size data while the second one allows for online data available in real time. It will be shown that these methods provide consistent and asymptotically Gaussian estimates having asymptotic variance equal to that of the quasi-maximum likelihood estimate (QMLE) regardless of the value of the weighting parameter. Finite-sample performances of the proposed WLS estimates are shown via a simulation study for various sub-classes of power ARCH models.

Suggested Citation

  • Aknouche, Abdelhakim & Al-Eid, Eid M. & Hmeid, Aboubakry M., 2011. "Offline and online weighted least squares estimation of nonstationary power ARCH processes," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1535-1540, October.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1535-1540
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    References listed on IDEAS

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    7. Linton, Oliver & Pan, Jiazhu & Wang, Hui, 2010. "Estimation For A Nonstationary Semi-Strong Garch(1,1) Model With Heavy-Tailed Errors," Econometric Theory, Cambridge University Press, vol. 26(01), pages 1-28, February.
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    9. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
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    Cited by:

    1. Francq, Christian & Zakoian, Jean-Michel, 2013. "Inference in non stationary asymmetric garch models," MPRA Paper 44901, University Library of Munich, Germany.
    2. Abdelhakim Aknouche, 2012. "Multistage weighted least squares estimation of ARCH processes in the stable and unstable cases," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 241-256, October.
    3. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.

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