Abstract:
The Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models help to model
volatility and capture the most common properties such as volatility clustering, leptokurtosis and
the leverage effects which are exhibited by financial time series data. Asymmetric GARCH
models in particular are able to capture all the three main features that characterize financial data
unlike the basic symmetric Autoregressive Conditional Heteroscedasticity (ARCH)/GARCH
models. In the bulk of literature available for the asymmetric GARCH models, the maximum
likelihood estimation method has been the most preferred in parameter estimation due to its
simplicity and desirable propenies. However, this method is based on distributional assumptions
which are ofien violated in practice and thus alternative parameter estimation procedures are
required. In this research, optimal estimating functions which incorporate higher order moments
common in most financial time series data have been constructed for the asymmetric GARCH
class of models. Using a simulation study, it is shown that the estimating functions approach
competes favourably well with the maximum likelihood estimation method in estimation of the
asymmetric GARCH models especially in cases where non-Gaussian error distributions are
assumed. Funhennore, the estimating functions approach proves to be robust to distributional
assumptions as indicated by the minimal change in the mean square errors of the estimates across
different error distributions. Asset retum volatilities of the USA and Japan stock markets have
been modelled under both estimation methods utilising the S&P 500 index and the Nikkei 225
index datascts respectively. Empirical results show that the estimating functions approach is
more efficient especially in non-nonnal cases as indicated by the substantially lower standard
errors of the parameter estimates. Further. the volatilities are forecasted under the estimating
functions approach in which case the Exponential GARCH (EGARCH) model generally gives a
better out-of-sample fit than the Glosten, Jagannathan and Runkle — GARCH (GJR — GARCH)
model based on Mean Square Error (MSE) and Mean Absolute Error (MAE) loss functions.
Results from this study present an altemative estimation method that is more efficient and robust
to the classical maximum likelihood estimation method for the asymmetric GARCH models.
