Overview: MVGC computational pathways

The diagram below, adapted from the MVGC Toolbox reference document> [1] (Section 3) illustrates key computational pathways implemented in the toolbox.

A great deal of effort has gone into identifying useful, accurate and numerically efficient computational pathways; these are represented as bold arrows in the diagram. Blue arrows represent actual Granger causality computation, while the dashed arrow represents simulation for testing purposes. The pink shaded circles represent the equivalent VAR representations [1], while the Ann label computational algorithms implemented in the toolbox (see table below).

See the mvgc_demo script for a demonstration of how this works out in practice.

Contents

Data structures

See also common variable names and data structures in the MVGC help page.

namedescription
Xmultivariate (possibly multi-trial) time series data
A,SIGVAR parameters (coefficients and residuals covariance)
Gautocovariance sequence
Scross-power spectral density (cpsd)
FGranger causality (time domain)
fGranger causality (frequency domain)

Algorithms

 descriptionimplementation
A1 estimate autocovariance sequence from time series data tsdata_to_autocov
A2 estimate VAR model from time series data tsdata_to_var
tsdata_to_infocrit
A3 simulate (multiple) VAR processess var_to_tsdata
var_to_tsdata_nonstat
A4 estimate cpsd from time series data tsdata_to_cpsd
A5 calculate autocovariance sequence from VAR parameters var_to_autocov
A6 calculate VAR parameters from autocovariance sequence autocov_to_var
A7 calculate VAR parameters from cpsd cpsd_to_var
A8 calculate cpsd from VAR parameters var_to_cpsd
A9 calculate cpsd from autocovariance sequence (fft) autocov_to_cpsd
A10 calculate autocovariance sequence from cpsd (ifft) cpsd_to_autocov
A11 transform autocovariance for reduced regression autocov_xform
A12 transform cpsd for reduced regression cpsd_xform
A13 calculate time-domain causality from VAR parameters var_to_autocov
autocov_to_var
autocov_to_mvgc
autocov_to_pwcgc
A14 calculate frequency-domain (spectral) causality from VAR parameters and cpsd var_to_autocov
autocov_to_var
autocov_xform
autocov_to_smvgc
autocov_to_spwcgc
A15 calculate (band-limited) time-domain causality from spectral causality (integrate) smvgc_to_mvgc

References

[1] L. Barnett and A. K. Seth, The MVGC Multivariate Granger Causality Toolbox: A New Approach to Granger-causal Inference, J. Neurosci. Methods 223, 2014 [ preprint ].