Risk Measures and Time Series Data

Extreme events are phenomena that generally occur rarely but with significant, sometimes catastrophic impacts on the environment and society. Examples are tropical cyclones, tor-nadoes, floods, heat waves, wildfires and severe earthquakes, among many others. Model-ling extreme events is a challenging task as by their very nature the available data on them are scarce, which requires extrapolations outside the data range. Extreme value theory is a discipline in statistics where focus is on inferring about characteristics related to the tail of distribution functions, and hence it provides the natural framework for modelling extreme events. Catastrophic climate events like floods, wildfires, heatwaves are often the result of the simultaneous extreme behaviour of several interacting processes. The combination of processes leading to a significant impact is referred to as a compound event. Traditionally, climate science research has though focused on single drivers or univariate dangers, reduc-ing the complexity of climate dynamics and possible consequences. However, compound risk reflects the chance of many interacting climate causes or hazards, and hence these should be considered simultaneously in statistical analyses. Since in compound events sev-eral factors are jointly extreme it is for a proper understanding of them crucial to develop extreme value methods in a multivariate context, and this is the major aim of this project. In the recent extreme value literature, several estimators for multivariate risk measures have been introduced and studied, though the developed theory is typically under the assump-tion that we have a random sample available to base the estimation upon. However, within climate science, data are often collected over time (temperature, rainfall, ozone, pollution, ...)  and hence they show temporal dependence, which violates the standard assumption of independent observations. In the project it is the intention to go beyond this classical setup of independent observations and study the estimation of risk measures based on time se-ries data. With our study we contribute to establish advanced statistical models that enable climate researchers to better predict and understand the effect of extreme events like heat waves on ecosystems. 

 

Interested candidates should have a PhD in statistics or probability theory, with a solid background in extreme value statistics, stochastic processes and/or time series. Familiarity with statistical programming in R or a related software is an advantage.