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arXiv physics/0505074physics.soc-phq-fin.ST
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大部分股票市场的相关矩阵不是纯噪声

The bulk of the stock market correlation matrix is not pure noise

J. Kwapien, P. Oswiecimka, S. Drozdz

摘要:

我们分析了股票市场相关矩阵的特征值随代表价格变化的时间序列长度增加的分布结构。我们使用100个高资本化的股票从美国市场和相关的结果,相应的Wishart随机矩阵的合奏。事实证明,系统地,更多的特征值停留在随机矩阵理论(RMT)的这种变体所规定的边界之外。这可能表明,即使是股市相关矩阵的大部分频谱也带有某种相关性,当用于构建矩阵的时间序列较短时,这些相关性被测量噪声所掩盖。我们还研究了“带噪”特征信号的一些其他特征,如它们的回波分布、时间相关性或多重分形谱,结果支持了上述结论。

英文摘要:

We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and relate result to the corresponding ensemble of Wishart random matrices. It turns out that systematically more eigenvalues stay beyond the borders prescribed by this variant of the Random Matrix Theory (RMT). This may indicate that even the bulk of the spectrum of the stock market correlation matrix carries some sort of correlations that are masked by a measurement noise when the time series used to construct the matrix are short. We also study some other characteristics of the "noisy" eigensignals, like their return distributions, temporal correlations or their multifractal spectra and the results support the above conclusions.

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