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...

T his empirical analysis endeavors to trace out the causal nexus between core inflation and economic growth from the perspective of twenty worlds’ leading economy with the help of the nonlinear Granger causality approach by using time series data from 1981 to 2016. Based on nonlinear Granger causality results, it has been found that there is unidirectional casualty running from core ...

This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We present the definitions based on cond...

This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries. Using realistic (neural mass) models of coupled neuronal dynamics, we evaluate the robustness of parametric and nonparametric Granger causality. Starting from a broad class of generative (state-space) models of neuronal dynamics, we show how their Volterra kern...

Understanding of brain functioning requires the investigation of activated cortical networks, in particular the detection of interactions between different cortical sites. Commonly, coherence and correlation are used to describe interrelations between EEG signals. However, on this basis, no statements on causality or the direction of their interrelations are possible. Causality between two sign...

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have...