Abstract

Statistics of extremes is concerned with developing theoretically justified models for estimating the frequency and magnitude of rare catastrophic events such as heatwaves, stock market crashes, flooding, and structural failure of bridges. A central challenge in this area is modelling extremal dependence when several variables are involved.
The conditional extremes model of Heffernan and Tawn (2004) provides a flexible framework for modelling the conditional distribution of a random vector given that one of its components exceeds a high threshold, and is widely used due to the broad range of dependence structures it can accommodate. In this talk, we discuss how this framework can be adapted to the time series setting.
In particular, we present a methodology for modelling and simulating the behaviour of a stationary time series after it enters an extreme state, that is, following exceedance of a critical threshold. The fitted model naturally supports Monte Carlo estimation of quantities of interest, such as the expected duration of extreme episodes. We illustrate the methodology through estimation of cluster functionals for a time series of daily maximum temperatures observed in Orl´eans, France.
Finally, we briefly discuss recent developments and ongoing work, including the use of a Box–Cox–type transformation to reduce the nonlinear structure of the conditional extremes model to a more tractable linear form.