Abstract
Modelling extreme events requires statistical methods that can capture rare, high-impact observations under evolving conditions. Classical methods in Extreme Value Theory (EVT) provide powerful tools for characterising tail behaviour, but these approaches typically assume that the underlying process is stationary. This assumption is often unrealistic in applied settings, where distributional properties may evolve over time or vary with covariates. This thesis develops statistical methodologies designed to account for such non-stationarity, enabling more accurate and adaptive modelling of extreme behaviour in complex settings.This thesis makes contributions in three areas. First, a clustering-based approach is proposed for capturing covariate-driven non-stationarity, using Gaussian mixtures to partition the input space and fitting Generalised Pareto Distributions (GPDs) within each region. Second, a Bayesian framework is developed for detecting temporal non-stationarity in multiple time series via changepoints and cluster allocation, allowing for dynamic modelling of tail behaviour. Third, a new algorithm, Generalised Pareto ED-PELT (GPEP), is introduced for univariate changepoint detection in heavy-tailed time series, combining the strengths of parametric and non-parametric methods.
These frameworks are evaluated through simulation studies and an application to financial data, demonstrating improved inference of tail risk under evolving conditions. Together, they provide a flexible foundation for modern extreme value analysis in the presence of structural change.
| Date of Award | 22 Apr 2026 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Christian Rohrbeck (Supervisor) & Matthew Nunes (Supervisor) |
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