bootstrap_tsdata_to_pwcgc

Calculate sampling distribution for pairwise-conditional time-domain MVGCs from time series data, based on a nonparametric bootstrap

Syntax

   FB = bootstrap_tsdata_to_pwcgc(U,p,nsamps,acmaxlags,acdectol)

Arguments

See also Common variable names and data structures.

input

   U          multi-trial time series data
   p          model order (number of lags)
   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 Granger causalities (empirical distribution)

Description

Returns nsamps samples from the empirical sampling distribution of the pairwise-conditional time-domain MVGCs from 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 indexes the target (causee) variable and the third the source (causal) variable.

For usage in construction of GC confidence intervals, see mvgc_demo_bootstrap.

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_smvgc | bootstrap_tsdata_to_spwcgc | var_to_autocov | autocov_to_pwcgc.