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

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Jun Ma
Abstract

This paper presents a closed-form asymptotic variance-covariance matrix of the Maximum Likelihood Estimators (MLE) for the GARCH(1,1) model. Starting from the standard asymptotic result, a closed form expression for the information matrix of the MLE is derived via a local approximation. The closed form variance-covariance matrix of MLE for the GARCH(1,1) model can be obtained by inverting the information matrix. The Monte Carlo simulation experiments show that this closed form expression works well in the admissible region of parameters.

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Paper provided by University of Washington, Department of Economics in its series Working Papers with number UWEC-2006-11-R.

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Date of creation: Oct 2006
Date of revision: Oct 2006
Handle: RePEc:udb:wpaper:uwec-2006-11-r

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