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

This paper proposes the SU-normal distribution to describe non-normality features embedded in financial time series, such as: asymmetry and fat tails. Applying the SU-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 SU-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 SU-normal distribution. The exceeding ratio (ER) test results indicate that the SU-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.