Abstract
The generalized autoregressive conditionally heteroskedastic (GARCH) models are widely used for risk management when modelling the conditional variance of financial returns. GARCH processes have peculiar extremal properties, as extreme values tend to cluster according to a non trivial scheme. Marginal and dependence features of GARCH processes are determined by a multivariate regular variation property and tail processes. For high-order processes new results are presented and a set of new algorithms is analysed. These algorithms exploit a mixture of new limit theory and particle filtering results for fixed point distributions, so that a novel method is now available. Special cases including ARCH and IGARCH processes are investigated even when the innovation term is Skew-t distributed. In some of these special cases the marginal variance does not even exist. With our results it is possible to evaluate the marginal tail index and other measure of temporal extremal dependence, like the extremogram and the extremal index. The presentation will revise some published results as well as some ongoing research.
Collegamento Microsoft Teams
Organizzazione
Luca Trapin