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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 allows 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.

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