  Lead-lag relationships among assets represent a useful tool for analyzing
high frequency financial data. However, research on these relationships
predominantly focuses on correlation analyses for the dynamics of stock prices,
spots and futures on market indexes, whereas foreign exchange data have been
less explored. To provide a valuable insight on the nature of the lead-lag
relationships in foreign exchange markets here we perform a detailed study for
the one-minute log returns on exchange rates through three different
approaches: i) lagged correlations, ii) lagged partial correlations and iii)
Granger causality. In all studies, we find that even though for most pairs of
exchange rates lagged effects are absent, there are many pairs which pass
statistical significance tests. Out of the statistically significant
relationships, we construct directed networks and investigate the influence of
individual exchange rates through the PageRank algorithm. The algorithm, in
general, ranks stock market indexes quoted in their respective currencies, as
most influential. In contrast to the claims of the efficient market hypothesis,
these findings suggest that all market information does not spread
instantaneously.
