Feature ranking and network analysis of global financial indices.

The feature ranking method of machine learning is applied to investigate the feature ranking and network properties of 21 world stock indices. The feature ranking is the probability of influence of each index on the target. The feature ranking matrix is determined by using the returns of indices on a certain day to predict the price returns of the next day using Random Forest and Gradient Boosting. We find that the North American indices influence others significantly during the global financial crisis, while during the European sovereign debt crisis, the significant indices are American and European. The US stock indices dominate the world stock market in most periods. The indices of two Asian countries (India and China) influence remarkably in some periods, which occurred due to the unrest state of these markets. The networks based on feature ranking are constructed by assigning a threshold at the mean of the feature ranking matrix. The global reaching centrality of the threshold network is found to increase significantly during the global financial crisis. Finally, we determine Shannon entropy from the probabilities of influence of indices on the target. The sharp drops of entropy are observed during big crises, which are due to the dominance of a few indices in these periods that can be used as a measure of the overall distribution of influences. Through this technique, we identify the indices that are influential in comparison to others, especially during crises, which can be useful to study the contagions of the global stock market.