Extreme Value Theory: Dependence Effects

This lecture delves into the extremal index, a key concept in extreme value theory, exploring its implications for stationary processes. The extremal index characterizes the dependence structure of extremes, showing how it impacts the sizes of extreme events. The lecture also discusses the D'(u) condition, which governs short-range dependence and its relevance in modeling extreme events for various processes. The interplay between strong dependence at realistic levels and asymptotic independence is highlighted, along with conditions like D'', D(2), aiding in specific calculations.