英文标题：
《Symbolic dynamics techniques for complex systems: Application to share
  price dynamics》
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作者：
Dan Xu and Christian Beck
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最新提交年份：
2017
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英文摘要：
  The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Our main example is the investigation of share price returns in a coarse-grained way. A nontrivial spectrum of Renyi entropies is found. We study how the spectrum depends on the time scale of returns, the sector of stocks considered, as well as the number of symbols used for the symbolic description. Overall our analysis confirms that in the symbol space transition probabilities of observed share price returns depend on the entire history of previous symbols, thus emphasizing the need for a modelling based on non-Markovian stochastic processes. Our method allows for quantitative comparisons of entirely different complex systems, for example the statistics of symbol sequences generated by share price returns using 4 symbols can be compared with that of genomic sequences.
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中文摘要：
符号动力学技术因低维动力系统和混沌映射而闻名，是动力系统热力学形式主义的根源。在这里，我们表明，这种技术也可以成功地应用于由高维复杂系统生成的时间序列。我们的主要例子是以粗粒度的方式研究股价回报。发现了Renyi熵的一个非平凡谱。我们研究了频谱如何依赖于回报的时间尺度、所考虑的股票部门以及用于符号描述的符号数量。总体而言，我们的分析证实，在符号空间中，观察到的股价回报的转移概率取决于之前符号的整个历史，因此强调需要基于非马尔可夫随机过程的建模。我们的方法允许对完全不同的复杂系统进行定量比较，例如，使用4个符号的股价回报生成的符号序列的统计数据可以与基因组序列的统计数据进行比较。
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分类信息：

一级分类：Physics        物理学
二级分类：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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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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