Measures of Conditional Linear Dependence and Feedback between Time Series

Geweke, John

doi:10.1080/01621459.1984.10477110

Cited by 575 publications

(389 citation statements)

References 11 publications

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“…According to (10) the VAR coefficients A k may then be recovered from H(λ) by a matrix inversion and inverse Fourier transform. A further technical condition for valid G-causality analysis is that the CPSD be uniformly bounded away from zero almost everywhere (Geweke, 1982(Geweke, , 1984. Explicitly, there must exist a c > 0 such that for almost all 0 ≤ λ ≤ 2π…”

Section: Var Process Theorymentioning

confidence: 99%

“…Importantly, condition (11) guarantees square summability of the regression coefficients (Geweke, 1982(Geweke, , 1984Rozanov, 1967). Equations (6-10) relate the VAR parameters (A k , Σ), the autocovariance sequence Γ k and the CPSD S (λ).…”

Section: Var Process Theorymentioning

confidence: 99%

“…A powerful feature of G-causality is that it may be decomposed in a natural way by frequency (Geweke, 1982(Geweke, , 1984. The resulting spectral G-causality integrates to the time-domain causality previously introduced, which may thus be considered an average over all frequencies of the spectral causality.…”

Section: G-causality In the Frequency Domainmentioning

confidence: 99%

“…The MVGC toolbox facilitates both techniques; we recommend the former due to improved numerical accuracy and computational efficiency (Section 3.1 and Appendix A.1). As regards statistical inference, in contrast to the time-domain case there are (to our knowledge) no known (asymptotic) distributions for the sample distribution off Y→X (λ) (see Geweke, 1984 for a fuller discussion on this issue) and nonparametric techniques are best deployed for significance testing and derivation of confidence intervals 13 .…”

Section: G-causality In the Frequency Domainmentioning

confidence: 99%

“…Wiener-Granger causality (G-causality) (Granger, 1969;Geweke, 1982Geweke, , 1984 is an increasingly popular method for identifying "causal" connectivity in neural time series data (Bressler and Seth, 2011). It can be traced conceptually to Wiener (Wiener, 1956) and was operationalised by Granger in terms of linear autoregressive modelling of stochastic processes (Granger, 1969).…”

Section: Introductionmentioning

confidence: 99%

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The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

Barnett

Seth

2014

Journal of Neuroscience Methods

859

874

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Background: Wiener-Granger causality ("G-causality") is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling.New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s):The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions:The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.

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Section: Var Process Theorymentioning

confidence: 99%

Section: Var Process Theorymentioning

confidence: 99%

Section: G-causality In the Frequency Domainmentioning

confidence: 99%

Section: G-causality In the Frequency Domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

Barnett

Seth

2014

Journal of Neuroscience Methods

859

874

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Granger Causality: Basic Theory and Application to Neuroscience

Ding

Chen

Bressler

2006

Handbook of Time Series Analysis

535

521

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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 that neural interactions are directional. Being able to assess the directionality of neuronal interactions is thus a highly desired capability for understanding the cooperative nature of neural computation. Research over the last few years has shown that Granger causality is a key technique to furnish this capability. The main goal of this article is to provide an expository introduction to the concept of Granger causality. Mathematical frameworks for both bivariate Granger causality and conditional Granger causality are developed in detail with particular emphasis on their spectral representations. The technique is demonstrated in numerical examples where the exact answers of causal influences are known.It is then applied to analyze multichannel local field potentials recorded from monkeys performing a visuomotor task. Our results are shown to be physiologically interpretable and yield new insights into the dynamical organization of large-scale oscillatory cortical networks.

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