[量化金融] 分数高斯噪声的水平交叉分析 [推广有奖]

摘要翻译：
所谓的水平交叉分析已经被用来调查经验数据集。但对平交结果所反映的内容缺乏解释。分数高斯噪声作为一个定义明确的随机序列，可以作为一个合适的基准，使水平交叉的发现更有意义。本文计算了从对数（零Hurst指数，h=0)到高斯（h=1,($0<h<1$)的分数高斯噪声的平均上交叉频率。通过引入原始数据的总上移数相对于所谓的洗牌数据$\mathcal{R}$的相对变化，建立了Hurst指数与$\mathcal{R}$的经验函数。最后，为了使概念更加清晰，我们将该方法应用于一些金融序列。
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英文标题：
《Analysis of fractional Gaussian noises using level crossing method》
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作者：
M. Vahabi, G. R. Jafari, M. Sadegh Movahed
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最新提交年份：
2011
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分类信息：

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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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：
  The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make the level crossing findings more sense. In this article, we calculated the average frequency of upcrossing for a wide range of fractional Gaussian noises from logarithmic (zero Hurst exponent, H=0), to Gaussian, H=1, ($0<H<1$). By introducing the relative change of the total numbers of upcrossings for original data with respect to so-called shuffled one, $\mathcal{R}$, an empirical function for the Hurst exponent versus $\mathcal{R}$ has been established. Finally to make the concept more obvious, we applied this approach to some financial series.
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PDF链接：
https://arxiv.org/pdf/1112.1502