英文标题：
《Transition from lognormal to chi-square superstatistics for financial
  time series》
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作者：
Dan Xu and Christian Beck
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最新提交年份：
2016
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英文摘要：
  Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale of days, on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics. The system dynamics thus exhibits a transition from lognormal to chi-square superstatistics as a function of time scale. We discuss a more general model interpolating between both statistics which fits the observed data very well. We also present results on correlation functions of the extracted superstatistical volatility parameter, which exhibits exponential decay for returns on large time scales, whereas for returns on small time scales there are long-range correlations and power-law decay.
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中文摘要：
不同时间尺度上的股价回报可以用超统计动力学很好地建模。在这里，我们提供了一项调查，哪种类型的超统计学最适合恰当地描述不同时间尺度上的股价动态。研究表明，尽管卡方超统计学在日的时间尺度上运行良好，但在小得多的分钟时间尺度上，对数正态超统计学能更好地描述价格变化。因此，作为时间尺度的函数，系统动力学表现出从对数正态到卡方超统计的转变。我们讨论了一个更通用的模型，它在两个统计数据之间进行插值，非常适合观测数据。我们还展示了提取的超统计波动率参数的相关函数的结果，该参数在大时间尺度上表现出指数衰减，而在小时间尺度上表现出长期相关性和幂律衰减。
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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：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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