Mutual Information-Based Hierarchies on Warsaw Stock Exchange

A popular method for network analysis of financial markets is a notable part of econophysics research. The networks created in such efforts are focused exclusively on linear correlations between stocks. While Pearson's correlation is the obvious starting point, it would be useful to look at its alternatives as to whether they provide improvements to this methodology, particularly given Pearson's correlation coefficient considers only a limited class of association patterns. We propose to use mutual information-based hierarchical networks, as mutual information is a natural generalisation of Pearson's correlation. We estimate mutual information using naive plug-in estimator as consistent bias is not harmful to this application, however other methods may also be used. We then transform the mutual information into an Euclidean metric and create minimal spanning trees and maximally filtered planar graphs. We apply this methodology to Warsaw Stock Exchange for years between 2000 and 2013, and comment on the differences with the standard methodology, as well as the structural changes on Warsaw Stock Exchange which the study reveals.