Easily Adaptable Complexity Measure for Finite Time Series

Abstract

We present a complexity measure for any finite time series. This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the widely accepted but conflicting criteria for complexity measurements. Surprisingly, the measure is developed from Kolmogorov complexity, which is traditionally believed to represent only randomness and to satisfy one criterion to the exclusion of the others. For familiar iterative systems, our treatment may imply a heuristic approach to transforming symbolic dynamics into permutation dynamics and vice versa.