Causal Non-Linear Financial Networks

In our previous study we have presented an approach to studying lead--lag effect in financial markets using information and network theories. Methodology presented there, as well as previous studies using Pearson's correlation for the same purpose, approached the concept of 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 effects. To incorporate causality in a manner consistent with our previous study, that is including non-linear interdependencies, we base this study on a generalisation of Granger causality in the form of transfer entropy, or equivalently a special case of conditional (partial) mutual information. This way we are able to produce networks of stocks, where directed links represent causal relationships for a specific time lag. We apply this procedure to stocks belonging to the NYSE 100 index for various time lags, to investigate the short-term causality on this market, and to comment on the resulting Bonferroni networks.