Extremal behavior of finite EGARCH processes

Abstract

Extreme value theory for a class of EGARCH processes is developed. It is shown that the EGARCH process as well as the logarithm of its conditional variance lie in the domain of attraction of the Gumbel distribution. Norming constants are obtained and it is shown that the considered processes exhibit the same extremal behavior as their associated iid sequences. The results are then compared to related models, such as stochastic volatility models or Log-ACD models