摘要翻译:
我们研究了与多元学生(或更一般的椭圆)随机变量有关的一个新的随机相关矩阵系综。我们建立了经验相关矩阵的精确态密度,推广了Marcenko-Pastur的结果。学生案例中的理论态密度与经验金融数据之间的比较出奇地好,即使我们仍然能够检测到系统偏差。最后,我们详细地计算了经验学生矩阵的Kullback-Leibler熵,这些熵与高斯情形下的真相关矩阵无关。我们给出了这些Kullback-Leibler熵的精确数值。
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英文标题:
《The Student ensemble of correlation matrices: eigenvalue spectrum and
Kullback-Leibler entropy》
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作者:
Giulio Biroli, Jean-Philippe Bouchaud and Marc Potters
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最新提交年份:
2007
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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:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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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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英文摘要:
We study a new ensemble of random correlation matrices related to multivariate Student (or more generally elliptic) random variables. We establish the exact density of states of empirical correlation matrices that generalizes the Marcenko-Pastur result. The comparison between the theoretical density of states in the Student case and empirical financial data is surprisingly good, even if we are still able to detect systematic deviations. Finally, we compute explicitely the Kullback-Leibler entropies of empirical Student matrices, which are found to be independent of the true correlation matrix, as in the Gaussian case. We provide numerically exact values for these Kullback-Leibler entropies.
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PDF链接:
https://arxiv.org/pdf/0710.0802