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摘要翻译：
能源市场和相关的能源期货市场在全球经济中发挥着至关重要的作用。本文研究了四种NYMEX能源期货的日波动率时间序列的重现间隔的统计性质，其定义为连续波动率超过给定阈值$q$之间的等待时间$\tau$。我们发现，循环间隔呈伸展指数$P_q(\tau)\sim e^{(a\tau)^{-\gamma}}$分布，其中指数$\gamma$随$q$的增加而减小，并且在不同阈值下，循环间隔按平均循环间隔$\bar\tau$缩放后，不存在缩放行为。这些发现在Kolmogorov-Smirnov检验和Crm{\'e}r-von Mises检验下是有意义的。我们证明了从上一个超过$q$的事件经过时间$t$之后的一个（短）时间间隔内，下一个超过阈值$q$的事件的发生概率$w_q(\delta{t}t)$的经验估计与数值积分结果非常一致。我们还研究了重复间隔对记忆的影响。结果表明，大、小递归区间的条件分布不同，递归区间的条件均值按前一区间$\bar\tau(\tau0)/\bar\tau\sim(\tau0/\bar\tau)^\beta$的幂律标度，说明递归区间具有短期相关性。去中心化波动分析和去中心化移动平均分析进一步揭示了复发间隔具有长期相关性。我们确认波动率重现区间的“聚类”是由波动率中众所周知的长期相关性引起的。
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英文标题：
《Extreme value statistics and recurrence intervals of NYMEX energy
futures volatility》
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作者：
Wen-Jie Xie (ECUST), Zhi-Qiang Jiang (ECUST), and Wei-Xing Zhou
(ECUST)
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最新提交年份：
2012
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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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英文摘要：
Energy markets and the associated energy futures markets play a crucial role in global economies. We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are defined as the waiting times $\tau$ between consecutive volatilities exceeding a given threshold $q$. We find that the recurrence intervals are distributed as a stretched exponential $P_q(\tau)\sim e^{(a\tau)^{-\gamma}}$, where the exponent $\gamma$ decreases with increasing $q$, and there is no scaling behavior in the distributions for different thresholds $q$ after the recurrence intervals are scaled with the mean recurrence interval $\bar\tau$. These findings are significant under the Kolmogorov-Smirnov test and the Cram{\'e}r-von Mises test. We show that empirical estimations are in nice agreement with the numerical integration results for the occurrence probability $W_q(\Delta{t}|t)$ of a next event above the threshold $q$ within a (short) time interval after an elapsed time $t$ from the last event above $q$. We also investigate the memory effects of the recurrence intervals. It is found that the conditional distributions of large and small recurrence intervals differ from each other and the conditional mean of the recurrence intervals scales as a power law of the preceding interval $\bar\tau(\tau_0)/\bar\tau \sim (\tau_0/\bar\tau)^\beta$, indicating that the recurrence intervals have short-term correlations. Detrended fluctuation analysis and detrending moving average analysis further uncover that the recurrence intervals possess long-term correlations. We confirm that the "clustering" of the volatility recurrence intervals is caused by the long-term correlations well known to be present in the volatility.
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PDF链接：
https://arxiv.org/pdf/1211.5502
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