High-level dependence in time series models

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• 作者：Vicky Fasen ; Claudia Kl¨¹ppelberg and Martin Schlather
• 关键词：ARCH ; COGARCH ; Extreme cluster ; Extreme dependence measure ; Extremal index ; Extreme value theory ; GARCH ; Linear model ; Multivariate regular variation ; Nonlinear model ; L¨¦vy ; driven Ornstein– ; Uhlenbeck process ; Random recurrence equation
• 刊名：Extremes
• 出版年：2010
• 出版时间：March, 2010
• 年：2010
• 卷：13
• 期：1
• 页码：1-33
• 全文大小：601.0 KB

文摘

We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions to random recurrence equations; in particular, discrete and continuous-time moving average and (G)ARCH processes. To illustrate our results we present a small simulation study.