Measures of serial extremal dependence and their estimation
Measures of serial extremal dependence and their estimation
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DOI：
10.1016/j.spa.2013.03.014
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发表时间：
2013-03
影响因子：
1.4
通讯作者：
R. Davis;T. Mikosch;Yuwei Zhao
中科院分区：
文献类型：
--
作者：
R. Davis;T. Mikosch;Yuwei Zhao
本文的目的有两个：（1）我们回顾了严格平稳时间序列中序列极值相关的经典和最新测度及其估计。(2)我们讨论了最近的重尾时间序列的概念，包括经常变化和最大稳定过程。序列极值依赖的典型特征是序列中高阈值的不一致性簇。我们首先讨论的概念极值指数的一个单变量序列，即倒数的预期集群大小，这引起了极大的关注极值文献。然后，我们继续通过引入极值，这是一个渐近自相关函数的极值事件序列的时间序列。在这种情况下，我们讨论时间序列的规则变化。这个概念对于描述严格平稳序列中的序列极值依赖和重尾是有用的。我们简要讨论了由Basrak和Segers提出的用概率的方式描述规则变化序列的依赖结构的尾过程。具有Fréchet边缘的极大稳定过程是一类重要的正则变化序列。最近，这个类引起了建模和统计目的的关注。我们将极值图应用于最大稳定过程。最后讨论了时域和频域极值图的估计。
The goal of this paper is two-fold: (1) We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. (2) We discuss recent concepts of heavy-tailed time series, including regular variation and max-stable processes. Serial extremal dependence is typically characterized by clusters of exceedances of high thresholds in the series. We start by discussing the notion of extremal index of a univariate sequence, i.e. the reciprocal of the expected cluster size, which has attracted major attention in the extremal value literature. Then we continue by introducing the extremogram which is an asymptotic autocorrelation function for sequences of extremal events in a time series. In this context, we discuss regular variation of a time series. This notion has been useful for describing serial extremal dependence and heavy tails in a strictly stationary sequence. We briefly discuss the tail process coined by Basrak and Segers to describe the dependence structure of regularly varying sequences in a probabilistic way. Max-stable processes with Fréchet marginals are an important class of regularly varying sequences. Recently, this class has attracted attention for modeling and statistical purposes. We apply the extremogram to max-stable processes. Finally, we discuss estimation of the extremogram both in the time and frequency domains.