Time-dependent cross-correlations between different stock returns: a directed network of influence

We study the time-dependent cross-correlations of stock returns, i.e., we measure the correlation as the function of the time shift between pairs of stock return time series using tick-by-tick data. We find a weak but significant effect showing that in many cases the maximum correlation appears at nonzero time shift, indicating directions of influence between the companies. Due to the weakness of this effect and the shortness of the characteristic time (of the order of a few minutes), our findings are compatible with market efficiency. The interaction of companies defines a directed network of influence.