Maximum spanning tree (MST) is a popular tool in market network analysis. Large number of publications are devoted to the MST calculation and it's interpretation for particular stock markets. However, much less attention is payed in the literature to the analysis of uncertainty of obtained results. In the present paper we suggest a general framework to measure uncertainty of MST identification. We study uncertainty in the framework of the concept of random variable network (RVN). We consider different correlation based networks in the large class of elliptical distributions. We show that true MST is the same in three networks: Pearson correlation network, Fechner correlation network, and Kendall correlation network. We argue that among different measures of uncertainty the FDR (False Discovery Rate) is the most appropriated for MST identification. We investigate FDR of Kruskal algorithm for MST identification and show that reliability of MST identification is different in these three networks. In particular, for Pearson correlation network the FDR essentially depends on distribution of stock returns. We prove that for market network with Fechner correlation the FDR is non sensitive to the assumption on stock's return distribution. Some interesting phenomena are discovered for Kendall correlation network. Our experiments show that FDR of Kruskal algorithm for MST identification in Kendall correlation network weakly depend on distribution and at the same time the value of FDR is almost the best in comparison with MST identification in other networks. These facts are important in practical applications.
翻译:最大范围树(MST)是市场网络分析中最受欢迎的工具。大量出版物用于MST的计算和对特定股票市场的诠释。然而,文献中很少注意分析所得结果的不确定性。在本文件中,我们建议了一个衡量MST识别不确定性的一般框架。我们在随机变量网络概念(RVN)的框架内研究不确定性。我们考虑到大类椭圆分布中基于不同关联的网络。我们显示,真正的MST在三个网络中是相同的:皮尔逊相关网络、Fechner相关网络和Kendall相关应用网络。我们说,在不同的不确定性计量中,FDR(False发现率)是用于确定MST的不确定性分析。我们调查Kruskal算法用于确定MST识别的不确定性,并表明MST识别的可靠性在这三个网络中尤其不同。对于Pearson相关网络而言,FDR基本上取决于股票回报的分布。我们证明,FDR与FDER的重要关联应用网络在假设中几乎不敏感。在KIRST网络中发现,KIRS的相对价值分析中,在KRIRS的模型分布中显示最有趣的现象。