  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.
