A Simplified Approach to Estimating Parameter of the GARCH (1,1) Model

Abstract

The paper aims to present a method of parameter estimation of the GARCH (1,1) model. This estimation problem involves computing the parameter estimates by maximizing the log-likelihood function. The Quasi-Newton method and an appropriate starting point for the iterations were used. The idea of contour plots was applied to find the initial values of the parameters for the iterative process. The method presented in this paper was illustrated using the Paris Bourse stock exchange and Thailand rubber data. The estimated parameters were compared to the values obtain using the Excel’s Solver, in order to know accurateness of the method presented. The results showed that, apart from the Excel’s Solver, applying the Quasi-Newton method together with the idea of contour plots provides an appropriate approach for parameter estimation of the GARCH (1,1) model. The parameters obtained was then used to estimate the volatility of the Paris Bourse stock exchange data and the results obtained was consistent with a previous study.