A complexity score derived from principal components analysis of nonlinear order measures

The generation of a global “complexity” score for numerical series was derived from a principal components analysis of a group of nonlinear measures of experimental as well simulated series. The concept of complexity was demonstrated to be independent from other descriptors of ordered series such as the amount of variance, the departure from normality and the relative nonstationarity; and to be mainly related to the number of independent elements (or operations) needed to synthesize the series. The possibility of having a univocal ranking of complexity for diverse series opens the way to a wider application of dynamical systems concepts in empirical sciences.