Computing algebraic transfer entropy and coupling directions via transcripts

José Amigó; Roberto Monetti; Beata Graff; Grzegorz Graff

doi:10.1063/1.4967803

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.

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DOI:: Digital Object Identifier (open in new tab) 10.1063/1.4967803
License: Copyright (2016 AIP Publishing)

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: CHAOS no. 26, edition 113115, pages 1 - 12,
ISSN: 1054-1500
Language:: English
Publication year:: 2016
Bibliographic description:: Amigó J., Monetti R., Graff B., Graff G.: Computing algebraic transfer entropy and coupling directions via transcripts// CHAOS. -Vol. 26, iss. 113115 (2016), s.1-12
DOI:: Digital Object Identifier (open in new tab) 10.1063/1.4967803
Verified by:: Gdańsk University of Technology