德国股票市场指数（DAX）与日油价时间序列的水平交叉与逆统计分析
The level crossing and inverse statistic analysis of German stock market index (DAX) and daily oil price time series
摘要：
给出了DAX指数和石油价格时间序列的水平交叉和逆统计分析。我们确定正斜率交叉点的平均频率$ν_α^+$，其中$T_α =1/ν_α^+ $是再次观察水平$α$的平均等待时间。我们估计概率$P(K, α)$，它为我们提供了在时间尺度$T_α$中观察到具有正斜率的水平$α$的$K$时间的概率。对于所分析的时间序列，我们发现最大$K$约为6。我们表明，通过使用水平交叉分析，可以估计如何DAX和石油时间序列将发展。我们对DAX和油价日志收益的增量进行了相同的分析（称为逆统计），并提供了等待时间的分布，以观察增量的某个水平。
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, $ν_α^+$, where $T_α =1/ν_α^+ $ is the average waiting time for observing the level $α$ again. We estimate the probability $P(K, α)$, which provides us the probability of observing $K$ times of the level $α$ with positive slope, in time scale $T_α$. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
