基于秩相关的金融收益最小生成树构造
Construction of Minimum Spanning Trees from Financial Returns using Rank Correlation
摘要：
由相关矩阵构造最小生成树是研究金融市场关系的常用方法。然而，关于这个主题的大多数工作倾向于使用皮尔逊相关系数，它依赖于正态假设，并且可能对异常值的存在很脆弱，这两种方法都不适合研究财务回报。在本文中，我们研究的推断MST从每日美国，英国和德国的金融回报率使用皮尔逊和两个等级相关的方法，斯皮尔曼和肯德尔的$τ$。使用这些秩方法构造的MST往往比使用Pearson相关性构造的MST更稳定，并且在数据集上保持更多的边缘。Pearson和秩MST之间的边缘一致性取决于市场的状态，但秩MST通常在任何时候都表现出很强的一致性。偏离单变量正态性可能与相关矩阵的变化有关，但更难以与MST的变化联系起来。与系数无关，树往往具有相似的拓扑结构。对于较大的市场，根据MST相关矩阵构建的投资组合的成交额比来自完整协方差矩阵的投资组合的成交额要小，但对于较小的德国市场则不然。利用自举方法，我们发现，使用秩相关构造的相关矩阵是更强大的，但有小的差异之间的鲁棒性的MST。
英文摘要：
The construction of minimum spanning trees (MSTs) from correlation matrices is an often used method to study relationships in the financial markets. However most of the work on this topic tends to use the Pearson correlation coefficient, which relies on the assumption of normality and can be brittle to the presence of outliers, neither of which is ideal for the study of financial returns. In this paper we study the inference of MSTs from daily US, UK and German financial returns using Pearson and two rank correlation methods, Spearman and Kendall's $τ$. MSTs constructed using these rank methods tend to be more stable and maintain more edges over the dataset than those constructed using Pearson correlation. The edge agreement between the Pearson and rank MSTs varies significantly depending on the state of the markets, but the rank MSTs generally show strong agreement at all times. Deviation from univariate normality can be related to changes in the correlation matrices but is more difficult to connect to changes in the MSTs. Irrelevant of coefficient, the trees tend to have similar topologies. Portfolios constructed from the MST correlation matrices have a smaller turnover than those from the full covariance matrix for the larger markets, but not for the smaller German market. Using a bootstrap method we find that the correlation matrices constructed using the rank correlations are more robust, but there is little difference between the robustness of the MSTs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
