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

We demonstrate that minority mechanisms arise in the dynamics of markets because of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use mixed Majority/Minority Games to illustrate that a vanishing price return autocorrelation function does not necessarily imply market efficiency. On the contrary, we stress that crucial differences might be present between correlations measured conditionally and unconditionally on external patterns in such models.