title: Computing algebraic transfer entropy and coupling directions via transcripts.
abstract: Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.
authors.affiliation: Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain.
authors.forename: José M
authors.initials: JM
authors.lastname: Amigó
authors.affiliation: IngSoft GmbH, 90403 Nuernberg, Germany.
authors.forename: Roberto
authors.initials: R
authors.lastname: Monetti
authors.affiliation: Department of Hypertension and Diabetology, Medical University of Gdansk, 80-952 Gdansk, Poland.
authors.forename: Beata
authors.initials: B
authors.lastname: Graff
authors.affiliation: Faculty of Applied Physics and Mathematics, Gdansk University of Technology, 80-233 Gdansk, Poland.
authors.forename: Grzegorz
authors.initials: G
authors.lastname: Graff