  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.
