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arXiv 1702.06191q-fin.ST
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金融数据中的关键性证据

Evidence for criticality in financial data

G. Ruiz López, A. Fernández de Marcos

摘要:

我们提供的证据表明,累积分布的绝对归一化收益的$100$美国公司的市价总值最高,揭示了一个关键的行为,为不同的时间尺度$Δt$。这种累积分布,根据各种复杂的-和金融-系统,可以通过$q$ -高斯的累积分布函数建模,在非广延统计力学的背景下,最大化非玻尔兹曼熵的分布函数。这些$q$ -高斯函数由两个参数表征,即$(q,β)$,它们由$Δt$唯一定义.从这些依赖关系中,我们发现了$q$和$β$之间的单调关系,这可以被视为临界性的证据。我们数值确定的各种指数表征这种临界性。

英文摘要:

We provide evidence that cumulative distributions of absolute normalized returns for the $100$ American companies with the highest market capitalization, uncover a critical behavior for different time scales $Δt$. Such cumulative distributions, in accordance with a variety of complex --and financial-- systems, can be modeled by the cumulative distribution functions of $q$-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These $q$-Gaussians are characterized by two parameters, namely $(q,β)$, that are uniquely defined by $Δt$. From these dependencies, we find a monotonic relationship between $q$ and $β$, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.

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。

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