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A Closed-Form Asymptotic Variance-Covariance Matrix for the Quasi-Maximum Likelihood Estimator of the Garch(1,1) Model

12 Pages Posted: 23 Mar 2006 Last revised: 5 May 2008

Jun Ma

Northeastern University - Department of Economics

Date Written: May 1, 2008

Abstract

This paper presents a closed-form asymptotic variance-covariance matrix of the Quasi-Maximum Likelihood Estimator (QMLE) for the GARCH(1,1) model. The robust 'sandwich' asymptotic variance matrix is shown to be a product of the function of higher moments of innovation and the inverse of negative expected Hessian, whose closed-form in terms of only model parameters is then derived via a local approximation. Taking inverse of it, the variance-covariance matrix is readily obtained. A Monte Carlo simulation experiment demonstrates that this analytical formula works well for both normal and non-normal innovations in admissible parameter regions.

Keywords: GARCH, Quasi-Maximum Likelihood Estimator, asymptotic variance-covariance matrix

JEL Classification: C12, 22

Suggested Citation

Ma, Jun, A Closed-Form Asymptotic Variance-Covariance Matrix for the Quasi-Maximum Likelihood Estimator of the Garch(1,1) Model (May 1, 2008). Available at SSRN: https://ssrn.com/abstract=889461 or http://dx.doi.org/10.2139/ssrn.889461

Jun Ma (Contact Author)

Northeastern University - Department of Economics ( email )

301 Lake Hall
360 Huntington Avenue
Boston, MA MA 02446
United States

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