autocov_xform
Transform autocovariance sequence for reduced regression
Syntax
G = autocov_xform(G,AR,SIGR,useFFT)
Arguments
See also Common variable names and data structures.
input
G autocovariance sequence AR VAR coefficients matrix for reduced regression SIGR residuals covariance matrix for reduced regression useFFT use FFT method (default: true)
output
G transformed autocovariance sequence
Description
Returns the autocovariance sequence G for a new variable defined as the residuals of a reduced regression, for a VAR with autocovariance sequence G. AR and SIGR are the coefficients matrices and residuals covariance matrix respectively of the reduced regression, which is is assumed to correspond to the first size(AR,1) indices of G.
If the useFFT flag is set (default), then the autocovariance sequence is converted to a cpsd via FFT (see autocov_to_cpsd), the transformation effected on the cpsd (cf. cpsd_xform) and the result converted back to an autocovariance sequence via IFFT (see cpsd_to_autocov). Otherwise, the autocovariance sequence is transformed by explicit convolution. The FFT method is generally more efficient than the convolution method, particularly if the number of autocovariance lags is large.
This function is crucial to the calculation of spectral causality in the conditional case; see autocov_to_smvgc, autocov_to_spwcgc. In theory, if the original autocovariance sequence is calculated to q lags - under the assumption that it may not have decayed sufficiently for k < q lags (see var_to_autocov) - then the transformed autocovariance sequence should be calculated to 2q lags. In practice we find that calculating to q lags is generally sufficient for good accuracy. To calculate G to higher lags, the simplest option is to reduce the acdectol parameter in the call to var_to_autocov (e.g. squaring it will effectively double the number of lags q to which G and hence G is calculated).
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 ].
See also
var_to_autocov | autocov_to_var | autocov_to_smvgc | autocov_to_spwcgc | cpsd_xform | autocov_to_cpsd | cpsd_to_autocov