Entropic and algebraic transcript-based tools in time series analysis
For researchers analyzing coupled time series, this provides a more effective tool for detecting synchronization, though the improvement is incremental.
The paper introduces a novel similarity distance based on the mean Kendall distance for analyzing coupled time series in algebraic representations, and shows it outperforms existing entropic and algebraic tools in detecting generalized synchronization.
Algebraic representations of time series are symbolic representations whose symbols belong to a finite group. Precisely, the framework of the present paper is the analysis of coupled time series in algebraic representations and, more generally, group-valued time series. The prototype of an algebraic representation is an ordinal representation, whose symbols are permutations, also called ordinal patterns in the context of time series analysis. In fact, permutations, endowed with function composition, build a group called a symmetric group. A simple way to harness the algebraic structure of the alphabet in such cases is the concept of transcript from one group element to another. Since transcripts involve two group elements, they are very suitable for studying couplings between time series in the same algebraic representation. In this paper, we outline several existing entropic and algebraic transcript-based tools for analyzing coupled time series and systems. In addition to entropy, the entropic tools include divergence, statistical complexity and mutual information. The algebraic tools comprise order classes and, most recently, the Cayley and Kendall distances. We use the detection of generalized synchronization in a well-studied coupled system to compare the performances of some of those tools. To this end, we also provide an alternative tool called the similarity distance between times series, which is a mean Kendall distance. We found that the novel similarity distance outperforms the other tools tested.