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...

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 ...

Barnett et al. in 2009 proved that Granger causality and transfer entropy causality measure are equivalent for time series which have a Gaussian distribution. Granger causality test is linear, while transfer entropy a non-linear test. Many biological and physical mechanisms show to have non-Gaussian distributions. In this paper we investigate under which conditions on probability density distri...

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...

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...

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...

Granger causality (GC) is a statistical notion of causal influence based on prediction via linear vector autoregression. For Gaussian variables it equivalent to transfer entropy, an information-theoretic measure time-directed information between jointly dependent processes. We exploit such equivalence and calculate exactly the local causality, i.e., profile transferred from driver target proces...

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...