GENERALIZED STATISTICAL COMPLEXITY MEASURE

Abstract

A generalized Statistical Complexity Measure (SCM) is a functional that characterizes the probability distribution P associated to the time series generated by a given dynamical system. It quantifies not only randomness but also the presence of correlational structures. We review here several fundamental issues in such a respect, namely, (a) the selection of the information measure [Formula: see text]; (b) the choice of the probability metric space and associated distance [Formula: see text]; (c) the question of defining the so-called generalized disequilibrium [Formula: see text]; (d) the adequate way of picking up the probability distribution P associated to a dynamical system or time series under study, which is indeed a fundamental problem. In this communication we show (point d) that sensible improvements in the final results can be expected if the underlying probability distribution is "extracted" via appropriate consideration regarding causal effects in the system's dynamics.