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...

It is well known that in a vector autoregressive (VAR) model Granger non-causality is characterized by a set of restrictions on the VAR coefficients. This characterization has been derived under the assumption of non-singularity of the covariance matrix of the innovations. This note shows that if this assumption is violated, then the characterization of Granger non-causality in a VAR model fail...

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...

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...

This paper examines the causality between concentration in banking industry and economic growth by using data across 15 countries named in "Iran outlook in 2025", over the period 2004-2011. Our aim is to assess whether the economy grows more or less rapidly in areas where the banking sector is more concentrated. The topic is motivated by the fact that the causality between concentration in bank...

Granger causality has been applied to explore predictive causal relations among multiple time series in various fields. However, the existence of non-stationary distributional changes among the time series variables poses significant challenges. By analysing a real dataset, we observe that factors such as noise, distribution changes and shifts increase the complexity of the modelling, and large...