Figure 1

Schematic representation of the model. Starting from an empirical set of time series \({\overline{W}}\), we construct its unbiased randomization by finding the probability measure P(W) on the phase space \({{\fancyscript {W}}}\) which maximises Gibbs’ entropy while preserving the constraints \(\{{{\fancyscript {O}}}_l({\overline{W}}) \}_{l=1}^L\) as ensemble averages. The probability distribution P(W) depends on L parameters that can be found by maximising the likelihood of drawing \({\overline{W}}\) from the ensemble. In the figure, orange, turquoise and black are used to indicate positive, negative or empty values of the entries \(W_{i t}\), respectively, while brighter shades of each color are used to display higher absolute values. As it can be seen, the distribution P(W) assigns higher probabilities to those sets of time series that are more consistent with the constraints and therefore more similar to \({\overline{W}}\). See²⁰ for a similar chart in the case of the canonical ensemble of complex networks.