The analysis of return series from financial markets is often based on the Peaks-over-threshold (POT) model. This model assumes independent and identically distributed observations and therefore a Poisson process is used to characterize the occurrence of extreme events. However, stylized facts...

We consider a class of linear regression model with extreme distribution noise. We show by a mean of point process technique that the asymptotic distribution of the maximum is the same as the one of the max of the noise process, under specific conditions.

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.