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.

翻译：对平稳时间序列内联合极值依赖结构的精确建模是一个具有挑战性的问题，在许多应用中至关重要。此前针对该问题的若干方法仅适用于时间序列中特定类型的极值依赖，例如渐近依赖或有限阶马尔可夫时间序列。本文基于近期概率论成果，发展了时间序列极值的统计方法，使我们能够灵活建模平稳时间序列在观测到极端事件后的衰减过程。尽管有限阶马尔可夫序列自然适用于本方法，但我们基于条件极值模型考虑了更广泛的框架，该框架允许时间序列中存在多种可能的依赖结构。我们考虑基于蒙特卡洛模拟的推断，并推导了常用重要性抽样方差的上界。通过模拟数据中的聚类泛函估计以及法国奥尔良日最高气温时间序列的实例分析，对所提方法进行了验证。