摘要翻译：
给出了DAX与油价时间序列的水平交叉和逆统计分析。我们确定正斜率交叉的平均频率$\nu_{\alpha}^+$，其中$t_{\alpha}=1/\nu_{\alpha}^+$是再次观察水平$\alpha的平均等待时间。我们估计概率$p(K,\alpha)$,它提供我们在时间尺度$t_{\alpha}$中观察到具有正斜率的水平$\alpha$的$K$倍的概率。对于分析的时间序列，我们发现最大值K$约为6。我们表明，通过水平交叉分析，可以估计DAX和石油时间序列将如何发展。我们对DAX和石油价格日志返回的增量进行了相同的分析（称为逆统计），并给出了等待时间的分布，以观察增量的某个水平。
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英文标题：
《The level crossing and inverse statistic analysis of German stock market
  index (DAX) and daily oil price time series》
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作者：
F. Shayeganfar, M. Holling, J. Peinke, and M. Reza Rahimi Tabar
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最新提交年份：
2011
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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 level crossing and inverse statistics analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, $\nu_{\alpha}^+$, where $T_{\alpha} =1/\nu_{\alpha}^+ $ is the average waiting time for observing the level $\alpha$ again. We estimate the probability $P(K, \alpha)$, which provides us the probability of observing $K$ times of the level $\alpha$ with positive slope, in time scale $T_{\alpha}$. For analyzed time series we found that maximum $K$ is about 6. We show that by using the level crossing analysis one can estimate how the DAX and oil time series will develop. We carry out same analysis for the increments of DAX and oil price log-returns,(which is known as inverse statistics) and provide the distribution of waiting times to observe some level for the increments.
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PDF链接：
https://arxiv.org/pdf/1001.4401