Price return auto-correlation and predictability in agent-based models of financial markets

We demonstrate that minority mechanisms arise in the dynamics of markets because of effects of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use minority games to illustrate that a vanishing price return auto-correlation function does not necessarily imply market efficiency. On the contrary, we stress the difference between correlations measured conditionally and unconditionally on external patterns.