Prediction accuracy and sloppiness of log-periodic functions

We show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series. This comes from their sloppiness, the squared residuals depending very much on some combinations of parameters and very little on other ones. The time of singularity that is supposed to give an estimate of the day of the crash belongs to the latter category. We discuss in detail why and how the fitting procedure must take into account the sloppy nature of this kind of model. We then test the reliability of LPPLs on synthetic AR(1) data replicating the Hang Seng 1987 crash and show that even this case is borderline regarding the predictability of the divergence time. We finally argue that current methods used to estimate a probabilistic time window for the divergence time are likely to be over-optimistic.     

Collective rationality and functional wisdom of the crowd in far-from-rational institutional investors

The average portfolio structure of institutional investors is shown to reproduce the structure which optimally accounts for transaction costs when investment constraints are weak. Strikingly, this result emerges even though these investors are not aware of the existence of such law and despite the fact that their aims and tools are very heterogeneous. This extends the so-called wisdom of the crowd to much more complex situations in two important ways. First, wisdom of the crowd also holds for whole functions instead of a point-wise estimates. Second, this shows that in socio-economic systems, the optimal individual choice may only be found when the diversity of individual decisions is averaged out. Thus, rationality at a collective level does not need nearly rational individuals with well-aligned incentives. Finally we discuss the importance of accounting for constraints when assessing the presence of wisdom of the crowd.

     

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.