Extremal behavior of finite EGARCH Processes

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.