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The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has be...

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Autores principales: Koutlis, Christos, Kugiumtzis, Dimitris
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7915465/
https://www.ncbi.nlm.nih.gov/pubmed/33567755
http://dx.doi.org/10.3390/e23020208
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author Koutlis, Christos
Kugiumtzis, Dimitris
author_facet Koutlis, Christos
Kugiumtzis, Dimitris
author_sort Koutlis, Christos
collection PubMed
description Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey–Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source.
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spelling pubmed-79154652021-03-01 The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series Koutlis, Christos Kugiumtzis, Dimitris Entropy (Basel) Article Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey–Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source. MDPI 2021-02-08 /pmc/articles/PMC7915465/ /pubmed/33567755 http://dx.doi.org/10.3390/e23020208 Text en © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Koutlis, Christos
Kugiumtzis, Dimitris
The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series
title The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series
title_full The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series
title_fullStr The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series
title_full_unstemmed The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series
title_short The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series
title_sort effect of a hidden source on the estimation of connectivity networks from multivariate time series
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7915465/
https://www.ncbi.nlm.nih.gov/pubmed/33567755
http://dx.doi.org/10.3390/e23020208
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