The goal of this study is to detect linear and nonlinear causal pathways toward climate change as measured by changes in global mean surface temperature sea level over time using a data-based approach contrast the traditional physics-based models. Monthly data on potential factors, including greenhouse gas concentrations, sunspot numbers, humidity, ice sheets mass, coverage, from January 2003 D...

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear in...

Identifying causal relations among simultaneously acquired signals is an important challenging task in time series analysis. The original definition of Granger causality was based on linear models, its application to nonlinear systems may not be appropriate. We consider an extension of Granger causality to nonlinear bivariate time series with the universal approximation capacity in reproducing ...

We recently proposed a new measure, termed Phase Slope Index (PSI), It estimates the causal direction of interactions robustly with respect to instantaneous mixtures of independent sources with arbitrary spectral content. We compared this method to Granger Causality for linear systems containing spatially and temporarily mixed noise and found that, in contrast to PSI, the latter was not able to...

Measures of the direction and strength of the interdependence among time series from multivariate systems are evaluated based on their statistical significance and discrimination ability. The best-known measures estimating direct causal effects, both linear and nonlinear, are considered, i.e., conditional Granger causality index (CGCI), partial Granger causality index (PGCI), partial directed c...

Abstract Most Granger causality analysis (GCA) methods still remain a two-stage scheme guided by different mathematical theories; both can actually be viewed as the same generalized model selection issues. Adhering to Occam's razor, we present unified GCA (uGCA) based on minimum description length principle. In this research, considering common existence of nonlinearity in functional brain netw...

To study the dynamical mechanism which generates Parkinsonian resting tremor, we apply coupling directionality analysis to local field potentials (LFP) and accelerometer signals recorded in an ensemble of 48 tremor epochs in four Parkinsonian patients with depth electrodes implanted in the ventro-intermediate nucleus of the thalamus (VIM) or the subthalmic nucleus (STN). Apart from the traditio...

Across geosciences, many investigated phenomena relate to specific complex 1 systems consisting of intricately intertwined interacting subsystems. Such dynamical com2 plex systems can be represented by a directed graph, where each link denotes an existence 3 of a causal relation, or information exchange between the nodes. For geophysical systems 4 such as global climate, these relations are com...

This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and the Hilbert–Schmidt norm of the cross-covariance operator) and transfer entropy, examining each method and comparing their theoretical properties, with spec...