We consider extension of Granger causality to nonlinear bivariate time series. In this frame, if the prediction error of the first time series is reduced by including measurements from the second time series, then the second time series is said to have a causal influence on the first one. Not all the nonlinear prediction schemes are suitable to evaluate causality, indeed not all of them allow t...

We propose model-free measures for Granger causality in mean between random variables. Unlike the existing measures, ours are able to detect and quantify nonlinear causal effects. The new measures are based on nonparametric regressions and defined as logarithmic functions of restricted and unrestricted mean square forecast errors. They are easily and consistently estimated by replacing the unkn...

The multivariate nonlinear Granger causality developed by Bai et al. (2010) (Mathematics and Computers in simulation. 2010; 81: 5-17) plays an important role in detecting the dynamic interrelationships between two groups of variables. Following the idea of Hiemstra-Jones (HJ) test proposed by Hiemstra and Jones (1994) (Journal of Finance. 1994; 49(5): 1639-1664), they attempt to establish a cen...

This study aims to investigate Granger causality between renewable energy consumption (REC) and economic growth (EG) for USA. To accomplish this objective and to add the stronger evidence to the controversial issue, the tests were done under a new framework that embeds wavelet analysis, a novel tool, in nonlinear causality test approaches developed recently. The classical linear causality test ...

It is shown that gravitational waves do not have nonphysical “ghost” states in the Relativistic Theory of Gravitation with graviton having nonzero rest mass due to the causality condition. It was shown in [1,2] that, in linearized theory of gravitation, introducing the rest mass of graviton for a field with spins 2 and 0 leads to nonphysical “ghost states” due to spin 0 when interpreting gravit...

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear c...

The concept of emergence is central to artificial life and complexity science, yet quantitative, intuitive, and easy-to-apply measures of emergence are surprisingly lacking. Here, I introduce a just such a measure, G-emergence, which operationalizes the notion that an emergent process is both dependent upon and autonomous from its underlying causal factors. G-emergence is based on a nonlinear t...

Attempts to identify causal interactions in multivariable biological time series (e.g., gene data, protein data, physiological data) can be undermined by the confounding influence of environmental (exogenous) inputs. Compounding this problem, we are commonly only able to record a subset of all related variables in a system. These recorded variables are likely to be influenced by unrecorded (lat...

Granger causality is a statistical concept of causality that is based on prediction. According to Granger causality, if a signal X1 "Granger-causes" (or "G-causes") a signal X2, then past values of X1 should contain information that helps predict X2 above and beyond the information contained in past values of X2 alone. Its mathematical formulation is based on linear regression modeling of stoch...

We address a consistency problem in the commonly used nonparametric test for Granger causality developed by Hiemstra and Jones (1994). We show that the relationship tested is not implied by the null hypothesis of Granger non-causality. Monte Carlo simulations using processes satisfying the null hypothesis show that, for a given nominal size, the actual rejection rate may tend to one as the samp...