A comparative analysis of uncertainty conclusions on connections in the stock markets

The problem of connections' analysis between the stock returns is considered. The connections are measured by traditional Pearson correlation as well as rank Kendall correlation. Different measures of uncertainty conclusions on connections in the stock markets based on separation of the conclusions by significant and admissible are proposed. The proposed measures of uncertainty include the ratio of the number of insignificant but valid inferences to the total number of inferences and the ratio of the number of valid inferences to the number of significant inferences. These measures are divided into two types. Measures of the first type are defined as functions of the strength of the connection and provide detailed information on the change in the uncertainty of conclusions about connections in stock markets of a given strength. Measures of the second type or aggregate indicators of the uncertainty of conclusions about connections do not depend on the strength of the connection and characterize the uncertainty of the market as a whole. Comparison of uncertainty conclusions on connection in stock markets of Russia, USA and France is provided. It is shown that these markets differ slightly in the share of uncertain conclusions, regardless of the correlation coefficient used. At the same time, in terms of the number of admissible to the number of significant conclusions on connections, the Russian stock market is much more uncertain.