Modelling skewness and kurtosis with the skewed Gauss-Laplace sum distribution

An asymmetric extension of the recently proposed (symmetric) Gauss-Laplace sum distribution for stock returns is developed, motivated by the fact that many stock return distributions display significant asymmetries. The properties of the new distribution, insofar as relevant for estimation, testing, and the modelling of skewness and kurtosis, are derived. An application to three major US stock return indices shows an excellent fit of the model, which outperforms many popular alternatives.