英文标题：
《Minimum spanning tree filtering of correlations for varying time scales
and size of fluctuations》
---
作者：
Jaroslaw Kwapien, Pawel Oswiecimka, Marcin Forczek, Stanislaw Drozdz
---
最新提交年份：
2017
---
英文摘要：
Based on a recently proposed $q$-dependent detrended cross-correlation coefficient $\\rho_q$, we generalize the concept of minimum spanning tree (MST) by introducing a family of $q$-dependent minimum spanning trees ($q$MST) that are selective to cross-correlations between different fluctuation amplitudes and different time scales. They inherit this ability directly from the coefficients $\\rho_q$ that are processed here to construct a distance matrix. Conventional MST with detrending corresponds in this context to $q=2$. We apply the $q$MSTs to sample empirical data from the stock market and discuss the results. We show that the $q$MST graphs can complement $\\rho_q$ in disentangling correlations that cannot be observed by the MST graphs based on $\\rho_{\\rm DCCA}$ and, therefore, they can be useful in many areas where the multivariate cross-correlations are of interest. We apply our method to data from the stock market and obtain more information about correlation structure of the data than by using $q=2$ only. We show that two sets of signals that differ from each other statistically can give comparable trees for $q=2$, while only by using the trees for $q \\ne 2$ we become able to distinguish between these sets. We also show that a family of $q$MSTs for a range of $q$ express the diversity of correlations in a manner resembling the multifractal analysis, where one computes a spectrum of the generalized fractal dimensions, the generalized Hurst exponents, or the multifractal singularity spectra: the more diverse the correlations are, the more variable the tree topology is for different $q$s. Our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes, while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry.
---
中文摘要：
基于最近提出的$q$依赖的去趋势互相关系数$\\rho\\u q$，我们通过引入一系列的$q$依赖的最小生成树（$q$MST）来推广最小生成树（MST）的概念，这些树对不同波动幅度和不同时间尺度之间的互相关具有选择性。它们直接从这里处理的系数$\\rho\\u q$继承此能力，以构造距离矩阵。在这种情况下，带有detrending的传统MST对应于$q=2$。我们应用$q$MST从股票市场中抽取实证数据，并对结果进行讨论。我们表明，$q$MST图可以补充$\\rho\\u q$在基于$\\rho\\u{\\ rm DCCA}$的MST图无法观察到的分离相关性，因此，它们可以在多变量互相关感兴趣的许多领域中使用。我们将我们的方法应用于股票市场的数据，并获得了有关数据相关性结构的更多信息，而不是仅使用$q=2$。我们表明，统计上彼此不同的两组信号可以给出$q=2$的可比树，而只有使用$q=2$的树，我们才能区分这些组。我们还表明，一系列$q$MST（范围为$q$）以类似多重分形分析的方式表示相关性的多样性，其中计算广义分形维数、广义赫斯特指数或多重分形奇点谱：相关性的多样性越大，对于不同的q$s，树拓扑的变量越大。我们的分析表明，属于相同或类似工业部门的股票通过中等幅度的波动相互关联，而最大的波动往往发生在不一定属于同一行业的股票中。
---
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
--
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。
--

---
PDF下载：
-->