GARCH Processes with Skewed and Leptokurtic Innovations: Revisiting the Johnson SU Case

Abstract

We revisit the specification of GARCH processes with Johnson Su innovations examined in Choi and Nam (2008). This model, allowing for skewed and leptokurtic innovations, has many advantages over well known alternatives. We examine a simpler version of their specification which does not require the introduction of a location parameter. The likelihood function is derived and the model is estimated with the daily returns of six international stock indexes. The results show that the model provides an accurate fit using the past ten years of index returns which include the recent turbulent periods of the sub-prime and European sovereign debt crisis.

Keywords: GARCH, Johnson distributions, skewness, kurtosis

JEL Classification: C58, G17