Multichannel least-squares linear regression provides a fast, accurate, unbiased and robust estimation of Granger causality for neurophysiological data

The most common method for calculating Granger causality requires the fitting of a system of autoregressive equations to multiple interrelated signals. Historically, the Levinson, Wiggins, Robinson (LWR) algorithm and the least-squares linear regression (LSLR) approach are the most widely used methods for fitting these autoregressive equations. In this manuscript we compare these algorithms head-to-head. LSLR, as implemented using the Dynamic Autoregressive Neuromagnetic Causal Imaging (DANCI) method, was faster, and produced better residual error, normality, independence, and autocorrelation functions when analyzing real magnetoencephalography signals. Simulations demonstrated that the accuracy of LSLR was much higher than the LWR method and that the LSLR method, at least as implemented by DANCI, could accurately resolve the causal connectivity of 50 interrelated signals. We conclude that the multichannel LSLR method, as implemented by DANCI, can accurately calculate the interdependencies among multiple signals and has the potential to accurately calculate Granger causality for large-scale neurophysiological networks.