Estimation of Asymmetric Garch Models: The Estimating Functions Approach
Mr. Timothy Ndonye Mutunga, Prof. Ali Salim Islam, Dr. Luke Akong’o Orawo

Abstract
This paper introduces the method of estimating functions (EF) in the estimation of the Asymmetric GARCH family of models. This approach utilises the third and fourth moments which are common in financial time series data analysis and does not rely on distributional assumptions of the data. Optimal estimating functions have been constructed as a combination of linear and quadratic estimating functions. Estimates from the estimating functions approach are better than those of the traditional estimation methods such as the maximum likelihood estimation (MLE) especially in cases where distributional assumptions on the data are highly violated. We investigate the presence of asymmetric (leverage) effects in empirical time series and fit two of the most popular Asymmetric GARCH models (EGARCH and GJR-GARCH) under both the MLE and EF approaches. An empirical example demonstrates the implementation of the EF approach to Asymmetric GARCH models assuming a student’s – t distribution for the innovations. The efficiency benefits of the EF approach relative to the MLE method in parameter estimation are substantial for non-normal cases.

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