A Closed-Form Estimator For The Garch(1,1) Model
AbstractWe propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum likelihood estimator (QMLE) that it can be easily implemented and does not require the use of any numerical optimization procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T( 1) -consistency for some (1,2) when the fourth moment exists and -asymptotic normality when the eighth moment exists. We demonstrate that a finite number of Newton Raphson iterations using our estimator as starting point will yield asymptotically the same distribution as the QMLE when the fourth moment exists. A simulation study confirms our theoretical results.The first author s research was supported by the Shoemaker Foundation. The second author s research was supported by the Economic and Social Science Research Council of the United Kingdom.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 22 (2006)
Issue (Month): 02 (April)
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Cowles Foundation Discussion Papers
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- Amendola, Alessandra & Storti, Giuseppe, 2008. "A GMM procedure for combining volatility forecasts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3047-3060, February.
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- Christian M. Dahl & Emma M. Iglesias, 2008. "The limiting properties of the QMLE in a general class of asymmetric volatility models," CREATES Research Papers 2008-38, School of Economics and Management, University of Aarhus.
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