Testing for Nonlinearity Using Redundancies: Quantitative and Qualitative Aspects

A method for testing nonlinearity in time series is described based on information-theoretic functionals--redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique, also quantitative evaluation of dynamical properties of scrutinized data. An interplay of quantitative and qualitative testing on both the linear and nonlinear levels is analyzed and robustness of this combined approach against spurious nonlinearity detection is demonstrated.