Partially ordered permutation complexity of coupled time series

Abstract

A new information-theoretic complexity measure of coupling among multiple time series is proposed based on ordinal patterns. We regard ordinal patterns extracted from time series as total orders and exploit their algebraic properties to introduce a multiplication among them. The result of the multiplication is in general a partial order. A Kullback–Leibler divergence for the partial orders gives rise to a complexity measure of coupling in the sense that it vanishes in two extreme cases: when time series are uncoupled and when they are identical. The performance of the proposed complexity measure is tested on two model multivariate dynamical systems and its advantage over the existing complexity measures is discussed.