Extremal dependence measure and extremogram: the regularly varying case
Extremal dependence measure and extremogram: the regularly varying case
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极值依赖性测量和极值图：规则变化的情况
DOI：
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发表时间：
2012
期刊：
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通讯作者：
S. Resnick
中科院分区：
文献类型：
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作者：
Martin Larsson;S. Resnick
随机过程中大值的相依性是风险学、保险学和金融学中的一个重要课题。风险传染的思想是基于大价值依赖的思想。众所周知，高斯联结未能捕捉到这一现象。在过程或向量上下文中总结与相关函数相当的函数中的极端相关性的两个概念是极端相关性度量(EDM)和极值图。我们回顾了这些想法，并比较了两种工具，并以一个关于EDM的自然估计器的中心极限定理结束，该定理允许绘制可与经典样本相关函数背景下的Bartlett公式提供的置信度带相媲美的置信度带。
The dependence of large values in a stochastic process is an important topic in risk, insurance and finance. The idea of risk contagion is based on the idea of large value dependence. The Gaussian copula notoriously fails to capture this phenomenon. Two notions in a process or vector context which summarize extremal dependence in a function comparable to a correlation function are the extremal dependence measure (EDM) and the extremogram. We review these ideas and compare the two tools and end with a central limit theorem for a natural estimator of the EDM which allows drawing confidence bands comparable to those provided by Bartlett’s formula in a classical context of sample correlation functions.