Extreme Value Theory: Applications and Estimation

This lecture covers the application of Extreme Value Theory in statistical analysis, focusing on extremal limit theorems, point processes, Gaussian processes, Poisson processes, and multivariate extremes. The instructor discusses the theory and applications of extremes in time series, emphasizing the statistical analysis for extremes. Various estimation strategies, such as return level estimation and declustering, are explored, along with the importance of estimating the extremal index. The lecture also delves into modelling strategies using exceedances and the Generalized Pareto Distribution, highlighting the consequences of clustering in stationary series. The instructor demonstrates the estimation of extremal properties and return levels using empirical methods and bootstrap techniques.