金融相关性分析中的非对称矩阵
Asymmetric matrices in an analysis of financial correlations
摘要：
金融市场是一个高度相关的系统，它揭示了市场之间的依赖关系及其不同组成部分之间的相关性。标准分析技术包括信号对的相关系数和丰富的多元数据的相关矩阵。在后一种情况下，构造一个实对称矩阵，其实非负特征值描述数据的相关结构。然而，如果一个多变量数据进行相关函数的分析，当一个应力放在调查不同类型的信号之间的延迟依赖性，可以计算出一个非对称的相关矩阵与复杂的本征谱。从随机矩阵理论的角度来看，这类矩阵与Ginibre正交包络（GinOE）密切相关。我们提出了一个实际应用的例子，这种矩阵的相关性分析的经验数据。通过引入时滞，我们能够识别市场间相关性的时间结构。我们的研究结果表明，美国和德国的股票市场几乎同时演变，没有显着的时滞，所以很难找到这些市场之间的信息传递的印记。只有一个极其微妙的迹象表明，德国市场比美国市场领先几秒钟。
英文摘要：
Financial markets are highly correlated systems that reveal both the inter-market dependencies and the correlations among their different components. Standard analyzing techniques include correlation coefficients for pairs of signals and correlation matrices for rich multivariate data. In the latter case one constructs a real symmetric matrix with real non-negative eigenvalues describing the correlation structure of the data. However, if one performs a correlation-function-like analysis of multivariate data, when a stress is put on investigation of delayed dependencies among different types of signals, one can calculate an asymmetric correlation matrix with complex eigenspectrum. From the Random Matrix Theory point of view this kind of matrices is closely related to Ginibre Orthogonal Ensemble (GinOE). We present an example of practical application of such matrices in correlation analyses of empirical data. By introducing the time lag, we are able to identify temporal structure of the inter-market correlations. Our results show that the American and German stock markets evolve almost simultaneously without a significant time lag so that it is hard to find imprints of information transfer between these markets. There is only an extremely subtle indication that the German market advances the American one by a few seconds.
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