英文标题：
《Universality of market superstatistics》
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作者：
Mateusz Denys, Maciej Jagielski, Tomasz Gubiec, Ryszard Kutner, H.
Eugene Stanley
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最新提交年份：
2015
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英文摘要：
We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive \"superstatistics\" that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde)that exhibit transition thresholds. We measure the interevent times between excessive losses and excessive profits, and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a weighted sum of two components, (i) a powerlaw corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential, and (ii) a powerlaw damped by the upper incomplete gamma function, which tends toward the power-law only during short interevent times. We find that the scaling shape exponents that drive both components subordinate themselves and a \"superscaling\" configuration emerges. We use superstatistics to describe the hierarchical activity when component (i) reproduces the negative feedback and component (ii) reproduces the stylized fact of volatility clustering. Our results indicate that there is a functional (but not literal) balance between excessive profits and excessive losses that can be described using the same body of superstatistics, but different calibration values and driving parameters.
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中文摘要：
我们使用连续时间随机游走（CTRW）对交易员经历过度亏损或过度盈利时的市场波动数据进行建模。我们通过分析得出了“超统计学”，它精确地模拟了具有过渡阈值的经验市场活动数据（由Bogachev、Ludescher、Tsallis和Bunde提供）。我们测量了过度亏损和过度盈利之间的事件间隔时间，并使用平均事件间隔时间作为控制变量，得出了经验数据崩溃的通用描述。我们的超统计值是两个分量的加权和，（i）由较低的不完全伽马函数修正的幂律，其渐近趋向于稳健性，但最初给出指数；（ii）由较高的不完全伽马函数阻尼的幂律，其仅在短的事件间隔时间内趋向于幂律。我们发现，驱动这两个组件从属于自己的缩放形状指数出现了“超缩放”配置。当成分（i）再现负反馈，成分（ii）再现波动率聚类的程式化事实时，我们使用超统计来描述层次活动。我们的结果表明，超额利润和超额亏损之间存在函数（而非字面）平衡，可以使用相同的超统计体来描述，但校准值和驱动参数不同。
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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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