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.
The econophysics approach to socio-economic systems is based on the assumption of their complexity. Such assumption inevitably leads to another assumption, namely that underlying interconnections within socio-economic systems, particularly financial markets, are nonlinear, which is shown to be true even in mainstream economic literature. Thus it is surprising to see that network analysis of financial markets is based on linear correlation and its derivatives. An analysis based on partial correlation is of particular interest as it leads to the vicinity of causality detection in time series analysis. In this paper we generalise the planar maximally filtered graphs and partial correlation planar graphs to incorporate nonlinearity using partial mutual information.
We use multi-region Input-Output databases to show the sustainability of the Polish trade system. Analyses of the robustness of the supply system as a whole are missing in the literature, in strong contrast with a wide variety of network analyses inquiring into the resilience of financial systems. We represent the trade system as a flow network, and use information-theoretic approach to address growth and development of such a system. We perform an analysis of the development, robustness, and structural sustainability of the Polish trade system based on national Input-Output Tables (in current prices) for Poland for the years between 1995 and 2011. As such, we are also able to comment on the changes of the studied characteristics over the years. Further, we compare the results with the results obtained for the global supply system based on the multi-region Input-Output Tables. We find the Polish supply system to be much less organised than the global supply system. We also quantify the effect of the 2008 financial crisis on the size and organisation of the trade system in Poland.
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