cpsd_to_var

Spectral factorisation: calculate VAR parameters from cross-power spectral density

Syntax

   [H,SIG,iters] = cpsd_to_var(S,G0,maxiters,numtol)

Arguments

See also Common variable names and data structures.

input

   S          cross-power spectral density (cpsd) matrix
   G0         covariance matrix of VAR process (default: calculated automatically from cpsd)
   maxiters   maximum iterations (default: 100)
   numtol     numerical tolerance (default: 1e-10)

output

   H          VAR transfer function matrix
   SIG        VAR residuals covartiance matrix
   iters      number of iterations performed

Description

Calculates the transfer function H and residuals covariance matrix SIG from the cpsd S and covariance matrix G0 of a VAR process, using Wilson's spectral factorisation algorithm [2]. If G0 is not supplied (default), then G is calculated from S (see cpsd_to_autocov) and G0 set to G(:,:,1). The actual number of iterations performed is returned in iters. If the algorithm fails to converge to numerical tolerance numtol within maxiters iterations, an exception MVGC:XMaxItrs is thrown.

Note: to calculate the VAR coefficients, use the utility function trfun2var.

Adapted from original code with the kind permission of Prof. G. Rangarajan of the Dept. of Mathematics, Indian Institute of Science, Bangalore, India; see [3,4] for applications to Granger-causal analysis.

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] G. T. Wilson, "The factorization of matricial spectral densities", SIAM Journal on Applied Mathematics, 23(4), 1972.

[3] M. Dhamala, G. Rangarajan and M. Ding, "Estimating Granger causality from Fourier and wavelet transforms of time series data", Phys. Rev. Lett. 100, 2008.

[4] M. Dhamala, G. Rangarajan and M. Ding, "Analyzing information flow in brain networks with nonparametric Granger causality", NeuroImage 41, 2008.

See also

cpsd_to_autocov | autocov_to_var | trfun2var

Copyright notice

[(C)] Lionel Barnett and Anil K. Seth, 2012. See file license.txt in root directory for licensing terms.

MVGC Toolbox v1.0. © Lionel Barnett and Anil K. Seth, 2012.
See file license.txt for licensing terms.