Putting relative complexity estimates to work: a simple and general statistical methodology

Derivation of a general “distance-from-randomness” index for time series scaling with the relative complexity of an unknown generating system is presented. This index (SVSEn) corresponds to the Shannon entropy of the distribution of the eigenvalues of the correlation matrix derived by the embedding matrix of the series. The efficacy of the proposed index was tested by a number of simulations, demonstrating the possibility to derive a sensible complexity index without any strong theoretical constraint. Moreover SVSEn was demonstrated to have a direct relation with the relative complexity of the network system producing the series so allowing for a system identification approach on a strictly data-driven manner without any theoretical assumption.