Modelling the Clustering of Extreme Events for Short-Term Risk Assessment

Reliable estimates of the occurrence rates of extreme events are highly important for insurance companies, government agencies and the general public. The rarity of an extreme event is typically expressed through its return period, i.e. the expected waiting time between events of the observed size if the extreme events of the processes are independent and identically distributed. A major limitation with this measure is when an unexpectedly high number of events occur within the next few months immediately after a T year event, with T large. Such instances undermine the trust in the quality of risk estimates. The clustering of apparently independent extreme events can occur as a result of local non-stationarity of the process, which can be explained by covariates or random effects. We show how accounting for these covariates and random effects provides more accurate estimates of return levels and aids short-term risk assessment through the use of a complementary new risk measure. Supplementary materials accompanying this paper appear online.