Visibility graph combined with information theory: an estimator of stock market efficiency

The visibility graph (VG) is a technique that acts as a bridge between dynamic systems and graph theory, and has been applied in recent years to analyze different systems in an innovative way. In this paper, we use information theory quantifiers to analyze the graphs generated by the VG method as applied to the return rate time series of stock markets from different countries between 1995 and 2016. In particular, we consider the degree probability distribution of the generated graphs to calculate Shannon entropy and Fisher information, in order to build the Shannon–Fisher plane. By analyzing the pattern of the countries along this plot, we demonstrate by this methodology that, on average, developed countries are concentrated at the top right-hand side of the plane, while emerging countries appear mostly at the bottom of the plane; we also identify markets that form a community. Moreover, when a separate analysis is applied to data considering two periods (before and after 2008), it is possible to detect significant changes in the patterns, mainly for developed countries; this indicates a possible quantifier for the impact caused by the 2008 European crisis in the global markets.