engleski

Algorithms for Maximum Likelihood Estimation of GARCH Models

Analytical solution for the log-likelihood function maximization using first and second derivatives is too complex within GARCH type models. This paper examines NR, BHHH, BFGS and DFP as commonly used numerical algorithms. As solutions of different algorithms are sensitive to the initial values and convergence criteria, the contribution of this paper is to determine which algorithm gives the most stable estimates of the GARCH(1, 1) parameters with application to time series of daily returns from Zagreb Stock Exchange. This paper reveals advantages and disadvantages of different iteration procedures according to the approximation of the Hessian matrix.

GARCH(1 ; 1) ; maximum likelihood estimation ; Newton-Raphson ; BHHH ; BFGS ; DFP.

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