英文标题：
《An Empirical Method to Measure Stochasticity and Multifractality in
Nonlinear Time Series》
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作者：
Chih-Hao Lin, Chia-Seng Chang and Sai-Ping Li
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最新提交年份：
2014
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英文摘要：
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.
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中文摘要：
本文采用一种经验算法来研究非线性时间序列的随机性和多重分形性质。可以定义一个参数来定量测量时间序列与维纳过程的偏差，以便比较不同时间序列的随机性。利用该算法可以构造所研究时间序列的局部波动率，并利用该局部波动率分析时间序列的多重分形结构。作为一个例子，我们使用这种方法来分析不同股票市场的金融时间序列。结果表明，虽然发达市场的演化非常像一个Ito过程，但新兴市场远远没有效率。讨论了发达市场和新兴市场在多重分形结构和杠杆效应方面的差异。这里使用的算法可以以类似的方式应用于研究其他复杂系统的时间序列。
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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：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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