Time series conditional extremes

TL;DR

This paper introduces a flexible statistical methodology for modeling extremal dependence in stationary time series, accommodating various dependence structures beyond finite-order Markov models, with applications to temperature data.

Contribution

Develops a broad conditional extreme value model for time series that extends beyond existing methods limited to specific dependence types.

Findings

Effective estimation of cluster functionals in simulated data

Application to daily maximum temperature series from Orleans, France

Derived variance bounds for importance sampling

Abstract

Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types of extremal dependence in the time series such as asymptotic dependence, or Markov time series of finite order.\ In this paper, we develop statistical methodology for time series extremes based on recent probabilistic results that allow us to flexibly model the decay of a stationary time series after witnessing an extreme event.\ While Markov sequences of finite order are naturally accommodated by our approach, we consider a broader setup, based on the conditional extreme value model, which allows for a wide range of possible dependence structures in the time series.\ We consider inference based on Monte Carlo simulation and derive an upper bound for the variance of a commonly used importance sampler.\ Our methodology is illustrated via estimation of cluster functionals in simulated data and in a time series of daily maximum temperatures from Orleans, France.