Estimation of Volatility Parameters of GARCH(1,1) Models with Johnson’s SU distributed Errors

Abstract

This paper proposes a GARCH-type model allowing for time-varying volatility , skewness and kurtosis assuming a Johnson’s SU distribution for the error term. This distribution has two shape parameters and allow a wide range of skewness and kurtosis. We then impose dynamics on both shape parameters to obtain autoregressive conditional density (ARCD) models, allowing time-varying skewness and kurtosis. ARCD models with this distribution are applied to the daily returns of a variety of stock indices and exchange rates. Models with time-varying shape parameters are found to give better fit than models with constant shape parameters. Also a weighted forecasting scheme is introduced to generate the sequence of the forecasts by computing a weighted average of the three alternative methods suggested in the literature. The results showed that the weighted average scheme did not show clear superiority to the other three methods