title: Transcripts: an algebraic approach to coupled time series.
abstract: Ordinal symbolic dynamics is based on ordinal patterns. Its tools include permutation entropy (in metric and topological versions), forbidden patterns, and a number of mathematical results that make this sort of symbolic dynamics appealing both for theoreticians and practitioners. In particular, ordinal symbolic dynamics is robust against observational noise and can be implemented with low computational cost, which explains its increasing popularity in time series analysis. In this paper, we study the perhaps less exploited aspect so far of ordinal patterns: their algebraic structure. In a first part, we revisit the concept of transcript between two symbolic representations, generalize it to N representations, and derive some general properties. In a second part, we use transcripts to define two complexity indicators of coupled dynamics. Their performance is tested with numerical and real world data.
authors.affiliation: Centro de Investigación Operativa, Universidad Miguel Hernandez, Avda. de la Universidad s/n, 03202 Elche, Spain. jm.amigo@umh.es
authors.forename: José M
authors.initials: JM
authors.lastname: Amigó
authors.forename: Roberto
authors.initials: R
authors.lastname: Monetti
authors.forename: Thomas
authors.initials: T
authors.lastname: Aschenbrenner
authors.forename: Wolfram
authors.initials: W
authors.lastname: Bunk
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted