# Modelling the clustering of extreme events for short-term risk assessment

## TL;DR

This paper introduces a new approach to model the clustering of extreme events by incorporating covariates and random effects, improving short-term risk assessment and the reliability of extreme event estimates.

## Contribution

It presents a novel modeling framework that accounts for non-stationarity and clustering in extreme events, enhancing the accuracy of risk measures beyond traditional return periods.

## Key findings

- Clustering of extreme events can be explained by covariates and random effects.
- Accounting for these factors improves estimates of return levels.
- A new risk measure provides additional insights into short-term risk.

## Abstract

Having reliable estimates of the occurrence rates of extreme events is 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 \textit{T} year event, with \textit{T} large. Such events undermine the trust in the quality of these 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 new risk measure, which provides evidence of risk which is complementary to the return period.