英文标题：
《Multifractal Diffusion Entropy Analysis: Optimal Bin Width of
Probability Histograms》
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作者：
Petr Jizba and Jan Korbel
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最新提交年份：
2014
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英文摘要：
In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of R\\\'{e}nyi\'s entropy and the mean squared error analysis to discuss the conditions under which the error in the multifractal spectrum estimation is minimal. We illustrate the utility of our approach by focusing on a scaling behavior of financial time series. In particular, we analyze the S&P500 stock index as sampled at a daily rate in the time period 1950-2013. In order to demonstrate a strength of the method proposed we compare the multifractal $\\delta$-spectrum for various bin-widths and show the robustness of the method, especially for large values of $q$. For such values, other methods in use, e.g., those based on moment estimation, tend to fail for heavy-tailed data or data with long correlations. Connection between the $\\delta$-spectrum and R\\\'{e}nyi\'s $q$ parameter is also discussed and elucidated on a simple example of multiscale time series.
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中文摘要：
在多重分形扩散熵分析的框架下，我们提出了一种从感兴趣的潜在概率分布生成的直方图中选择最佳仓位宽度的方法。该方法利用R\\{e}nyi熵和均方误差分析技术讨论了多重分形谱估计误差最小的条件。我们通过关注金融时间序列的标度行为来说明我们方法的效用。特别是，我们分析了1950-2013年期间以日利率抽样的标准普尔500指数。为了证明所提出的方法的优点，我们比较了不同仓位宽度下的多重分形$\\delta$-谱，并展示了该方法的鲁棒性，尤其是对于$q$的大值。对于这些值，其他正在使用的方法，例如基于矩估计的方法，往往无法用于重尾数据或具有长相关性的数据。在一个简单的多尺度时间序列的例子中，还讨论并阐明了$\\delta$谱与R\\\'{e}nyi的$q$参数之间的关系。
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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：Mathematical Physics 数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics 数学
二级分类：Mathematical Physics 数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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