Granger-causal nonlinear financial networks

ABSTRACT Numerous attempts at studying the lead-lag effect in financial markets can be found in the literature, with recent attempts often using information and network theories. The methodology of these studies, based on Pearson's correlation coefficients or information-theoretic mutual information, approaches the concept of the lead-lag effect in a naive way. In this paper, we further investigate the lead-lag effect in financial markets, this time treating them as causal (in the Granger sense) effects, using transfer entropy. This way, we are able to produce networks of stocks in which directed links represent causal relationships for a specific time lag. We apply this procedure to stocks belonging to the Standard & Poor's 100 index for various time lags in order to investigate the short-term causality on this market. We find that causal relationships are more prevalent than lagged synchronization relationships in New York's market. We also observe that the number of statistically significant links dissipates quickly with increasing time lag. While networks of Granger-causal relationships on the studied market are not scale free, we find the distributions of significant transfer entropy values to be strongly fat tailed. ;