A multi-layer, multi-node ReLU network is a powerful, efficient, and popular tool in statistical prediction tasks. However, in contrast to the great emphasis on its empirical applications, its statistical properties are rarely investigated which is mainly due to its severe nonlinearity and heavy...

This paper investigates the performance of different parametric models, stable and tempered stable distributions, for capturing the tail behaviour of the log-returns. We first define and discuss the properties of the stable and tempered stable random variables. We then show how to estimate their...