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Granger causality has become an indispensable tool for analyzing causal relationships between time series. In this paper, we provide a detailed overview of its mathematical foundations, trace its historical development, and explore how…
At least two recent developments have put the spotlight on some significant gaps in the theory of multivariate time series. The recent interest in the dynamics of networks; and the advent, across a range of applications, of measuring…
Extracting causal connections can advance interpretable AI and machine learning. Granger causality (GC) is a robust statistical method for estimating directed influences (DC) between signals. While GC has been widely applied to analysing…
We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among…
This paper contributes to the understanding of strongly coupled spatio-temporal processes by describing a generic method based on Granger causality. The method is validated by the robust identification of causality regimes and of their…
Multivariate time series (MTS) forecasting is an essential problem in many fields. Accurate forecasting results can effectively help decision-making. To date, many MTS forecasting methods have been proposed and widely applied. However,…
Granger causality has been used for the investigation of the inter-dependence structure of the underlying systems of multi-variate time series. In particular, the direct causal effects are commonly estimated by the conditional Granger…
Granger causality is widely used for causal structure discovery in complex systems from multivariate time series data. Traditional Granger causality tests based on linear models often fail to detect even mild non-linear causal…
Granger causality is a commonly used method for uncovering information flow and dependencies in a time series. Here we introduce JGC (Jacobian Granger Causality), a neural network-based approach to Granger causality using the Jacobian as a…
We develop a multivariate functional autoregressive model (MFAR), which captures the cross-correlation among multiple functional time series and thus improves forecast accuracy. We estimate the parameters under the Bayesian dynamic linear…
Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks…
Dependence between nodes in a network is an important concept that pervades many areas including finance, politics, sociology, genomics and the brain sciences. One way to characterize dependence between components of a multivariate time…
Inferring causal relationships in observational time series data is an important task when interventions cannot be performed. Granger causality is a popular framework to infer potential causal mechanisms between different time series. The…
Granger Causality (GC) offers an elegant statistical framework to study the association between multivariate time series data. Vector autoregressive models (VAR) are simple and easy to fit, but have limited application because of their…
This is a comment to the paper 'A study of problems encountered in Granger causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical…
Granger causality method analyzes the time series causalities without building a complex causality graph. However, the traditional Granger causality method assumes that the causalities lie between time series channels and remain constant,…
Since interactions in neural systems occur across multiple temporal scales, it is likely that information flow will exhibit a multiscale structure, thus requiring a multiscale generalization of classical temporal precedence causality…
Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC)…
Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized…
With the advancement of deep learning technologies, various neural network-based Granger causality models have been proposed. Although these models have demonstrated notable improvements, several limitations remain. Most existing approaches…