极端事件的返回间隔分布与长时记忆

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摘要翻译：
在许多学科中，极端事件之间的重复时间或返回间隔的分布对于表征和理解物理系统和现象的行为具有重要意义。众所周知，自然界和社会中的许多物理过程都表现出长程关联。因此，在过去的几年里，大量的研究工作被用于研究长程相关时间序列的回归区间分布。数值模拟表明，回波间隔分布为伸展指数型。本文给出了长期相关时间序列中收益率区间分布的一个解析表达式，该表达式在平均收益率区间较大时成立。我们证明了分布实际上是幂律的乘积，是一个拉伸的指数形式。我们还讨论了有效性的机制，并详细研究了回报区间分布如何依赖于定义极端事件的阈值。
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英文标题：
《Return interval distribution of extreme events and long term memory》
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作者：
M. S. Santhanam and Holger Kantz
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最新提交年份：
2008
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long range correlations. Hence, in the last few years, considerable research effort has been directed towards studying the distribution of return intervals for long range correlated time series. Based on numerical simulations, it was shown that the return interval distributions are of stretched exponential type. In this paper, we obtain an analytical expression for the distribution of return intervals in long range correlated time series which holds good when the average return intervals are large. We show that the distribution is actually a product of power law and a stretched exponential form. We also discuss the regimes of validity and perform detailed studies on how the return interval distribution depends on the threshold used to define extreme events.
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PDF链接：
https://arxiv.org/pdf/0803.1706

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关键词：极端事件 distribution Econophysics correlations Mathematical 序列 间隔 series intervals 长程