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

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

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 10 (October)
    Pages: 1535-1540

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1535-1540
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    1. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    2. 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.
    3. Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
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    6. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, 03.
    7. Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
    8. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    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 575-96, May.
    10. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, 07.
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