Analysis of time series correlation. the choice of distance metrics and network structure

Abstract

Standard analysis of correlations between companies consists of two stages: calculating the distance matrix and construction of a chosen graph structure. In the paper the most often used Ultrametric Distance (UD) is compared with the Manhattan Distance (MD). It is showed that MD allows to investigate a broader class of correlation and is more robust to the noise influence. Therefore MD was used to construct entropy distance, which is applied to the analysis of correlation between subset of WIG20 and S&P500 companies. In the analysis three network structures were used: minimum spanning tree and unidirectional and bidirectional minimum length path. The results are compared to the standard UD based analysis. The advantages and disadvantages of the analysed time series distances are outlined.