ABSTRACT

In this paper, we propose an original method suitable for two-step assessment of the character of a time series under study. The first step is testing for nonlinearity in the data dynamics in a general sense, and the second step is identification of chaotic dynamics with the possibility of its subsequent quantification. The whole method is based on evaluation of so-called redundancies, information-theoretic functionals which have a special form for linear processes, and thus a comparison of their linear and general versions can demonstrate the linear or nonlinear nature of the data. On the other hand, when redundancies are estimated from chaotic data, they have specific properties reflecting a positive information production rate. This rate is measured by metric (Kolmogorov-Sinai) entropy that can be estimated directly from the redundancies. In this part of the method, i.e., in estimations of the metric entropy, we follow the original work of Fraser (1989b).