Ranking causal influence of financial markets via directed information graphs

A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed method represents the indices as nodes in a directed graph, where the edges' weights are estimates of the pair-wise causal influences, quantified using the directed information functional. This method facilitates using a relatively small number of samples from each index. The indices are then ranked according to their net-flow in the estimated graph (sum of the incoming weights subtracted from the sum of outgoing weights). Daily and minute-by-minute data from nine indices (three from Asia, three from Europe and three from the US) were analyzed. The analysis of daily data indicates that the US indices are the most influential, which is consistent with intuition that the indices representing larger economies usually exert more influence. Yet, it is also shown that an index representing a small economy can strongly influence an index representing a large economy if the smaller economy is indicative of a larger phenomenon. Finally, it is shown that while inter-region interactions can be captured using daily data, intra-region interactions require more frequent samples.