Title: The extremal index for IGARCH(p,q) processes with skewed innovations
Authors: Fabrizio Laurini - University of Parma (Italy) [presenting]
Abstract: GARCH process are widely used for modelling features commonly found in observed financial returns. The extremal properties of these processes are of wide interest for market risk management. Only for simple GARCH(1,1) extremes have been fully characterised, and much remains to be found about the dependence structure. In particular, the mean number of extreme values in a short term cluster, i.e., the reciprocal of the extremal index, has only been characterised in special cases which exclude all GARCH(p,q) processes that are used in practice, e.g., with innovations with unbounded support or asymmetry. Although recent research has identified the multivariate regular variation property of stationary GARCH(p,q) processes, currently there are no methods for numerically evaluating key components of these characterisations. We overcome these issues and are able to generate the forward tail chain of the process to derive the extremal index even for the general Integrated GARCH(p,q), considering unbounded and asymmetric innovations. The convergence of our numerical algorithm is very fast due to a efficient implementation of a particle filtering simulation technique.