Anja Janssen: The time change formula for extremes of stationary time series

A common assumption for modelling the extremal behavior of a stationary time series is to work in the framework of multivariate regular variation. In this setting, the extremal behavior of a time series can be described by the so-called tail process, which is the limiting distribution of the rescaled process, given an extreme event at time 0. It has been shown that stationarity of the underlying process implies a certain structure of the tail process, which is informally known as the "time change formula". We will explore how to construe this formula, analyze in which way the tail process describes the general extremal behavior of the underlying time series and discuss statistical interpretations.