Asymmetric and leptokurtic distribution for heteroscedastic asset returns: The S U -normal distribution

This paper proposes the S U -normal distribution to describe non-normality features embedded in financial time series, such as: asymmetry and fat tails. Applying the S U -normal distribution to the estimation of univariate and multivariate GARCH models, we test its validity in capturing asymmetry and excess kurtosis of heteroscedastic asset returns. We find that the S U -normal distribution outperforms the normal and Student- t distributions for describing both the entire shape of the conditional distribution and the extreme tail shape of daily exchange rates and stock returns. The goodness-of-fit (GoF) results indicate that the skewness and excess kurtosis are better captured by the S U -normal distribution. The exceeding ratio (ER) test results indicate that the S U -normal is superior to the normal and Student- t distributions, which consistently underestimate both the lower and upper extreme tails, and tend to overestimate the lower tail in general.