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arXiv 2207.03221q-fin.STphysics.data-an
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金融市场中的偏离集聚类

Clustering of Excursion Sets in Financial Market

M. Shadmangohar, S. M. S. Movahed

摘要:

利用偏移集理论,计算了股票市场指数的局部极值数密度和交叉统计量与阈值的关系。将数值计算的偏移集的数密度与高斯过程的理论预测进行比较,证实本文使用的所有数据集在低(高)阈值处几乎在平均值附近具有局部极值(上交)密度的盈余(几乎缺乏)值,这意味着股票指数的普遍性质。我们估计聚类的几何措施的基础上找到的对的偏移集,澄清以及位于同一地理区域的市场之间的统计一致性的超额概率。同时考虑了各市场间的漂移集的互相关性,构造了凝聚层次聚类矩阵。我们的研究结果表明,峰值统计是更能够捕获块。在此基础上,对包含峰和上交叉点的未加权两点相关函数的最大值的矩阵进行奇异值分解,计算相似性度量。我们的研究结果支持偏移集比标准措施更敏感,以阐明存在的{ \it先验}危机。

英文摘要:

Relying on the excursion set theory, we compute the number density of local extrema and crossing statistics versus the threshold for the stock market indices. Comparing the number density of excursion sets calculated numerically with the theoretical prediction for the Gaussian process confirmed that all data sets used in this paper have a surplus (almost lack) value of local extrema (up-crossing) density at low (high) thresholds almost around the mean value implying universal properties for stock indices. We estimate the clustering of geometrical measures based on the excess probability of finding the pairs of excursion sets, which clarify well statistical coherency between markets located in the same geographical region. The cross-correlation of excursion sets between various markets is also considered to construct the matrix of agglomerative hierarchical clustering. Our results demonstrate that the peak statistics is more capable of capturing blocks. Incorporating the partitioning approach, we implement the Singular Value Decomposition on the matrix containing the maximum value of unweighted Two-Point Correlation Function of peaks and up-crossing to compute the similarity measure. Our results support that excursion sets are more sensitive than standard measures to elucidate the existence of {\it a priori} crisis.

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