论文标题
金融协方差和相关性的新集体措施
New Collectivity Measures for Financial Covariances and Correlations
论文作者
论文摘要
复杂的系统通常是非平稳的，它们的动态通常由集体效应主导。集体性，定义为整个系统或其某些部分的连贯运动，在协方差和相关矩阵的时间依赖性结构中表现出来。最大的特征值对应于整个系统的集体运动，而另一个大型，孤立的，特征值表示系统部分中的集体性。就金融而言，这些是工业部门。通过删除整个系统的集体运动，后一种效果得到了更好的揭示。我们衡量剩余的集体性，我们称之为平均部门集体。我们确定雷曼兄弟周围的集体信号坠毁，以及互联网泡沫破裂之后。对于雷曼兄弟（Lehman Brothers）崩溃，我们发现了潜在的先驱。我们分析了从1990年到2021年的30多年的213个股票。我们绘制了平均部门的集体性与对应于最大特征值的集体性，以研究整个市场轨迹，这两种集体都跨越了二维空间。因此，我们以更精确的方式捕获了平均部门的集体。此外，我们观察到，平均部门集体中较大的值通常伴随着平均协方差和平均相关性的趋势变化。截至2015/2016年，美国股票市场的集体性发生了根本变化。
Complex systems are usually non-stationary and their dynamics is often dominated by collective effects. Collectivity, defined as coherent motion of the whole system or of some of its parts, manifests itself in the time-dependent structures of covariance and correlation matrices. The largest eigenvalue corresponds to the collective motion of the system as a whole, while the other large, isolated, eigenvalues indicate collectivity in parts of the system. In the case of finance, these are industrial sectors. By removing the collective motion of the system as a whole, the latter effects are much better revealed. We measure a remaining collectivity to which we refer as average sector collectivity. We identify collective signals around the Lehman Brothers crash and after the dot-com bubble burst. For the Lehman Brothers crash, we find a potential precursor. We analyze 213 US stocks over a period of more than 30 years from 1990 to 2021. We plot the average sector collectivity versus the collectivity corresponding to the largest eigenvalue to study the whole market trajectory in a two dimensional space spanned by both collectivities. Therefore, we capture the average sector collectivity in a much more precise way. Additionally, we observe that larger values in the average sector collectivity are often accompanied by trend shifts in the mean covariances and mean correlations. As of 2015/2016 the collectivity in the US stock markets changed fundamentally.
