In this equation, the two signals are predicted by a linear combination of their own past values, and the past values of the other time series. The residual errors (unexplained variance) are captured by the variables and , with covariance matrix . We estimated the coefficients for the VAR model by setting the order M=32 and using the armorf function in the BSMART toolbox62 to find the least-squares solution to equation (2). We then used the standard decomposition of Granger's time domain causality into frequency-domain Granger causality, as developed by Geweke et al.63. Fourier transformation of equation (2) yields the spectral decomposition
