Agenda

Speaker: Fabrizio Laurini, Università di Parma

Abstract:
Generalized autoregressive conditionally heteroskedastic (GARCH) processes, which are widely used for risk management when modelling the conditional variance of financial returns, 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 has Skew-t distribution. 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 is based on the paper: Laurini, F., Fearnhead, P. & Tawn, J. "Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes". Stat Comput 32, 104 (2022). https://doi.org/10.1007/s11222-022-10164-5 (available open access).

Bio Sketch:
Fabrizio Laurini is Professor in Economic Statistics at the University of Parma. He holds a PhD in Statistics Applied to Economics and Social Sciences from the University of Padua. His research focuses on the analysis of (economic) time series and their extremes.

The talk will also be available via Zoom https://unive.zoom.us/j/85153268624
Meeting ID: 851 5326 8624
Passcode: SanMarco2