bootstrap_tsdata_to_smvgc
Calculate sampling distribution for conditional frequency-domain MVGC from time series data, based on a nonparametric bootstrap
Syntax
fB = bootstrap_tsdata_to_smvgc(U,x,y,p,fres,nsamps,acmaxlags,acdectol)
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 (default: automatic) nsamps number of bootstrap samples acmaxlags maximum autocovariance lags (default as for 'var_to_autocov') acdectol autocovariance decay tolerance (default as for 'var_to_autocov')
output
fB bootstrap spectral Granger causalities (empirical distribution)
Description
Returns nsamps samples from the empirical sampling distribution of the frequency-domain MVGC from the variable Y (specified by the vector of indices y) to the variable X (specified by the vector of indices x), conditional on all other variables in the time series data U. The bootstrap randomly samples (with replacement) residuals of the full autoregression of U on its own lags; the subsampled residuals are then added back to the corresponding predictors to form surrogate time series [2]. p is the model order; for other parameters see var_to_autocov.
The first dimension of the returned matrix fB indexes samples, the second frequency.
Spectral causality is calculated up to the Nyqvist frequency at a resolution fres. If fres is not supplied it is calculated optimally as the number of autocovariance lags. Call freqs = sfreqs(fres,fs), where fs is the sampling rate, to get a corresponding vector freqs of frequencies on [0,fs/2].
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] D. A. Freedman, Bootstrapping regression models, Ann. Stats. 9(6), 1981.
See also
mvgc_demo_bootstrap | bootstrap_tsdata_to_mvgc | bootstrap_tsdata_to_pwcgc | bootstrap_tsdata_to_spwcgc | var_to_autocov | autocov_to_smvgc | sfreqs.