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A Closed-Form Estimator For The Garch(1,1) Model

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  • Kristensen, Dennis
  • Linton, Oliver

Abstract

We 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 Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 02 (April)
Pages: 323-337

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Handle: RePEc:cup:etheor:v:22:y:2006:i:02:p:323-337_06

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Cited by:
  1. Amendola, Alessandra & Storti, Giuseppe, 2008. "A GMM procedure for combining volatility forecasts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3047-3060, February.
  2. Sbrana, Giacomo & Poloni, Federico, 2013. "A closed-form estimator for the multivariate GARCH(1,1) model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 152-162.
  3. PREMINGER, Arie & HAFNER, Christian M., 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," CORE Discussion Papers 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Alessandra Amendola & Giuseppe Storti, 2009. "Combination of multivariate volatility forecasts," SFB 649 Discussion Papers SFB649DP2009-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Prono, Todd, 2011. "When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models," MPRA Paper 33593, University Library of Munich, Germany.
  6. HAFNER, Christian M. & PREMINGER, Arie, 2006. "Asymptotic theory for a factor GARCH model," CORE Discussion Papers 2006071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Donald W.K. Andrews & Patrik Guggenberger, 2011. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," Cowles Foundation Discussion Papers 1812, Cowles Foundation for Research in Economics, Yale University.
  8. 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.
  9. PREMINGER, Arie & STORTI, Giuseppe, 2006. "A GARCH (1,1) estimator with (almost) no moment conditions on the error term," CORE Discussion Papers 2006068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Stelios Arvanitis & Antonis Demos, 2014. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," DEOS Working Papers 1406, Athens University of Economics and Business.
  11. Leucht, Anne & Neumann, Michael H. & Kreiss, Jens-Peter, 2013. "A model specification test for GARCH(1,1) processes," Working Papers 13-11, University of Mannheim, Department of Economics.
  12. Todd, Prono, 2009. "Simple, Skewness-Based GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 30994, University Library of Munich, Germany, revised 30 Jul 2011.

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