Complexity of time series associated to dynamical systems inferred from independent component analysis

A not trivial problem for every experimental time series associated to a natural system is to individuate the significant variables to describe the dynamics, i.e., the effective degrees of freedom. The application of independent component analysis (ICA) has provided interesting results in this direction, e.g., in the seismological and atmospheric field. Since all natural phenomena can be represented by dynamical systems, our aim is to check the performance of ICA in this general context to avoid ambiguities when investigating an unknown experimental system. We show many examples, representing linear, nonlinear, and stochastic processes, in which ICA seems to be an efficacious preanalysis able to give information about the complexity of the dynamics.