中小规模财务数据分析
Medium and Small Scale Analysis of Financial Data
摘要：
金融数据的随机分析。特别是，我们调查如何统计的日志返回不同的时间延迟$τ$的变化。金融数据的规模依赖行为可以分为两个区域。第一个时间范围，即小时间尺度区域（以秒为单位）似乎具有普遍的特征。第二个时间范围，即从几分钟以上的中等时间尺度范围，可以用级联过程来表征，该级联过程由尺度$τ$中的随机马尔可夫过程给出。从给定的数据中可以提取出相应的Fokker-Planck方程，并提供了对金融数据复杂性的非平衡数学描述。
英文摘要：
A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays $τ$. The scale dependent behaviour of financial data can be divided into two regions. The first time-range, the small-timescale region (in the range of seconds) seems to be characterized by universal features. The second time-range, the medium-timescale range from several minutes upwards and can be characterized by a cascade process, which is given by a stochastic Markov process in the scale $τ$. A corresponding Fokker-Planck equation can be extracted from given data and provides a non equilibrium thermodynamical description of the complexity of financial data.
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