When Things Get Extreme: Records and Crashes

This contribution is concerned with statistical methods for analyzing extremes in univariate and multivariate time series. In particular, we discuss their use for the detection of global warming signals and assessing dependencies that typically arise in risk management. Multiple connections to the oeuvre of Wolfgang Schmid are indicated (The text is a translated, edited, expanded, and updated version of (Müller and Quatember, Wenn es extrem wird: Krachende Rekorde. In W. G. Müller, A. Quatember (Eds.), Fakt oder Fake? Wie Ihnen Statistik bei der Unterscheidung helfen kann (pp 149–161). Springer, 2022) by permission through Springer Nature license #5420800249333.).