金融数据的小尺度行为
Small scale behavior of financial data
摘要：
提出了一种新的方法来描述金融数据的日志返回分布的统计量的变化作为时间尺度的函数。为此，引入了一种度量，其量化所考虑的分布到参考分布的距离。一个小的时间尺度政权的存在证明，表现出不同的属性相比，正常的时间尺度政权。这种制度似乎对个股普遍适用。结果表明，这种小时标制度的存在是不依赖于距离测量或参考分布的特殊选择。这些发现对风险分析具有重要影响，特别是对极端事件的概率。
英文摘要：
A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered distribution to a reference distribution. The existence of a small timescale regime is demonstrated, which exhibits different properties compared to the normal timescale regime. This regime seems to be universal for individual stocks. It is shown that the existence of this small timescale regime is not dependent on the special choice of the distance measure or the reference distribution. These findings have important implications for risk analysis, in particular for the probability of extreme events.
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