Entropic and algebraic transcript-based tools in time series analysis

Abstract

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.

18 pages, 5 figures

References in corpus (15)

• Complex network approaches to nonlinear time series analysis
• ordpy: A Python package for data analysis with permutation entropy and ordinal network methods
• Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology
• Characterizing Synchronization in Time Series using Information Measures Extracted from Symbolic Representations
• On the Automatic Parameter Selection for Permutation Entropy
• Permutation Complexity via Duality between Values and Orderings
• Information directionality in coupled time series using transcripts
• Permutation complexity of interacting dynamical systems
• Estimation of the control parameter from symbolic sequences: Unimodal maps with variable critical point
• Kendall Tau Sequence Distance: Extending Kendall Tau from Ranks to Sequences
• Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate - blood pressure coupling quantified by entropy-based indices
• Statistical Properties of the Entropy from Ordinal Patterns
• Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks
• Permutation-Based Distances for Groups and Group-Valued Time Series
• Transcript-based estimators for characterizing interactions