Modelling conditional heteroskedasticity and skewness using the skew-normal distribution

The skew-normal distribution presents itself as a natural candidate for modelling conditional heteroskedasticity in financial time series since it generalises the normal distribution as a special case and departures from normality are skewed and leptokurtic. Conditional heteroskesdacity models are presented in addition to conditional skewness models. The skewness is regulated by a single parameter which is allowed to vary in an autoregressive manner. A generalisation of the GARCH-in-mean model is permitted to include the skewness parameter to capture any skewness premium in asset returns. Extensive empirical applications are applied to the FTSE Small Capitalisation Index.