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.
| name | description |
|---|---|
| X | multivariate (possibly multi-trial) time series data |
| A,SIG | VAR parameters (coefficients and residuals covariance) |
| G | autocovariance sequence |
| S | cross-power spectral density (cpsd) |
| F | Granger causality (time domain) |
| f | Granger causality (frequency domain) |
Algorithms
| description | implementation | |
|---|---|---|
| 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 ].