Financial networks based on Granger causality: A case study

Abstract

Connectivity analysis is performed on a long financial record of 21 international stock indices employing a linear and a nonlinear causality measure, the conditional Granger causality index (CGCI) and the partial mutual information on mixed embedding (PMIME), respectively. Both measures aim to specify the direction of the interrelationships among the international stock indexes and portray the links of the resulting networks, by the presence of direct couplings between variables exploiting all available information. However, their differences are assessed due to the presence of nonlinearity. The weighted networks formed with respect to the causality measures are transformed to binary ones using a significance test. The financial networks are formed on sliding windows in order to examine the network characteristics and trace changes in the connectivity structure. Subsequently, two statistical network quantities are calculated; the average degree and the average shortest path length. The empirical findings reveal interesting time-varying properties of the constructed network, which are clearly dependent on the nature of the financial cycle.