A Dynamic Extreme Value Model with Application to Volcanic Eruption Forecasting

Abstract Extreme events such as natural and economic disasters leave lasting impacts on society and motivate the analysis of extremes from data. While classical statistical tools based on Gaussian distributions focus on average behaviour and can lead to persistent biases when estimating extremes, extreme value theory (EVT) provides the mathematical foundations to accurately characterise extremes. This motivates the development of extreme value models for extreme event forecasting. In this paper, a dynamic extreme value model is proposed for forecasting volcanic eruptions. This is inspired by one recently introduced for financial risk forecasting with high-frequency data. Using a case study of the Piton de la Fournaise volcano, it is shown that the modelling framework is widely applicable, flexible and holds strong promise for natural hazard forecasting. The value of using EVT-informed thresholds to identify and model extreme events is shown through forecast performance, and considerations to account for the range of observed events are discussed.