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...

This paper examines the behavior of forecasts made from a co-integrated system as introduced by Granger (1981), Granger and Weiss (1983) and Engle and Granger (1987). It is established that a multi-step forecast will satisfy the co-integrating relation exactly and that this particular linear combination of forecasts will have a finite limiting forecast error variance. A simulation study compare...

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 ...

Power modulations of oscillations in electro- and magnetoencephalographic (EEG/MEG) signals have been linked to a wide range of brain functions. To date, most of the evidence is obtained by correlating bandpower fluctuations to specific target variables such as reaction times or task ratings, while the causal links between oscillatory activity and behavior remain less clear. Here, we propose to...

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and precisely estimate the Granger causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framewo...

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...

this paper examines the causal relationship between energy use and real gdp for the period 1967-2002 in iran. the results of phillips- perron test indicate that the real gdp and the four categories of energy, i.e. coal, oil, gas, and hydroelectric energy are integrated of order one. besides, the johansen — juselius maximum likelihood co- integration tests imply the existence of granger causalit...

Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes — Hawkes process. According to the relationship between Hawkes process’s impact function and its Granger causality graph, our model represents impact functions using a series of basis f...

Causal inference among high-dimensional time series data proves an important research problem in many fields. While in the classical regime one often establishes causality among time series via a concept known as “Granger causality,” existing approaches for Granger causal inference in high-dimensional data lack the means to characterize the uncertainty associated with Granger causality estimate...

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...