Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between s...

The traditional linear Granger test has been widely used to examine the linear causality among several time series in bivariate settings as well as multivariate settings. Hiemstra and Jones [19] develop a nonlinear Granger causality test in bivariate settings to investigate the nonlinear causality between stock prices and trading volume. This paper extends their work by developing a non-linear ...

A time series is said to Granger cause another series if it has incremental predictive power when forecasting it. While Granger causality tests have been studied extensively in the univariate setting, much less is known for the multivariate case. In this paper we propose multivariate out-of-sample tests for Granger causality. The performance of the out-of-sample tests is measured by a simulatio...

Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such relations. In this work we consider nonlinear extensions of Granger’s idea and refer to the result as Extended Granger Causality. A simple approach implementi...

It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger causality analysis may not clearly distinguish between direct causal influences from one time series to another and indirect ones acting through a third time ...

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate auto...

Granger causality methods were developed to analyze the flow of information between time series. These methods have become more widely applied in neuroscience. Frequency-domain causality measures, such as those of Geweke, as well as multivariate methods, have particular appeal in neuroscience due to the prevalence of oscillatory phenomena and highly multivariate experimental recordings. Despite...

In this paper, we discuss the properties of mixed graphs which visualize causal relationships between the components of multivariate time series. In these Granger-causality graphs, the vertices, representing the components of the time series, are connected by arrows according to the Granger-causality relations between the variables whereas lines correspond to contemporaneous conditional associa...