GCCA_tsdata_to_smvgc
Calculate unconditional frequency-domain MVGC (spectral multivariate Granger causality) from time series data by "traditional" method (as e.g. in GCCA toolbox)
Syntax
f = GCCA_tsdata_to_smvgc(U,x,y,p,fres,regmode)
Arguments
See also Common variable names and data structures.
input
U multi-trial time series data x vector of indices of target (causee) multi-variable y vector of indices of source (causal) multi-variable p model order (number of lags) fres frequency resolution regmode regression mode (default as in 'tsdata_to_var')
output
f unconditional spectral Granger causality
Description
Returns the unconditional frequency-domain (spectral) MVGC
from the variable Y (specified by the vector of indices y) to the variable X (specified by the vector of indices x) in the time series data U, for model order p.
NOTE: This routine will not compute conditional causalities, since the "traditional" full/reduced regression method may well produce unacceptably inaccurate (or nonesensical) results in the conditional case. For an analysis of the reasons for this, see [2,*]. For the same reason, there is no pairwise-conditional GCCA_tsdata_to_smvgc_pwc routine in this toolbox. Since conditional causalities are generally what you want (unconditional causalities may be highly misleading [1]), we strongly reccommend computation of conditional spectral MVGC using the preferred autocovariance-based approach; see autocov_to_smvgc.
Spectral causality is calculated up to the Nyqvist frequency at a resolution fres. Call freqs = sfreqs(fres,fs), where fs is the sampling rate, to get a corresponding vector freqs of frequencies on [0,fs/2]. The regression mode is set by the regmode parameter, which may be 'LWR' or 'OLS' (see tsdata_to_var for details and defaults).
This routine is included mainly for compatibility with the Granger Causal Connectivity Analysis (GCCA) Toolbox [3]; the preferred MVGC Toolbox method of calculating spectral MVGC via the autocovariance sequence (see autocov_to_smvgc) will generally be more accurate and, furthermore, will calculate conditional spectral causality.
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 ].
[2] Y. Chen, S. L. Bressler and M. Ding, "Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data", J. Neurosci. Methods, 150, 2006.
[3] A. K. Seth, "A MATLAB toolbox for Granger causal connectivity analysis", Journal of Neuroscience Methods 186, 2010.
[*] In our experience the "partition matrix" method in ref. [2] appears to be unsound, producing inaccurate results; hence we do not use it here.
See also
tsdata_to_var | var_to_cpsd | sfreqs | autocov_to_smvgc | isbad