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

DOI: 10.5772/intechopen.70506

Mohammed Elamin Hassan, Henry Mwambi and Ali Babikir Mohammed Elamin Hassan, Henry Mwambi

Additional information is available at the end of the chapter and Ali Babikir

http://dx.doi.org/10.5772/intechopen.70506 Additional information is available at the end of the chapter

### Abstract

Distributed Errors

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.

Keywords: GARCH models, conditional volatility, skewness and kurtosis
