Uncertainty of Market Graph Identification

One of the popular tools for analyzing network models of a market is the threshold similarity graph or market graph, which illustrates the strength and topology of correlations in the stock market. Several papers are devoted to the construction of such a graph in order to analyze correlations in specific stock markets. However, the reliability or uncertainty of the conclusions obtained has not been sufficiently studied. To carry out such studies, we investigate some measures of uncertainty. These measures include classical measures based on risk function and new measures based on recently proposed methods for dividing conclusions about correlations into two sets: a statistically significant set of conclusions and a statistically nonsignificant set of conclusions or zone of uncertainty. The paper shows the relationship of some new measures of uncertainty with classical ones. The proposed measures of uncertainty include the ratio of the size of the nonsignificant set of conclusions to the total number of conclusions and the ratio of the size of the nonsignificant set of conclusions to the size of the significant set of conclusions. These measures are divided into two types. Measures of the first type are defined as functions of the chosen threshold of the market graph. The measures of the second type, or uncertainty indicators, do not depend on the threshold of the threshold similarity graph. Data from 12 stock markets are used to investigate the proposed measures of uncertainty. The correlation is estimated using both the traditional Pearson correlation coefficient and the Kendall correlation coefficient.