Granger causality from first principles

Rather than using a black box (the GCCA toolbox), I implemented the Granger causality workflow in Matlab from first principles -- e.g. multivariate (vector) autoregressive modeling (VAR model). By working through the logic step-by-step, I have the basic framework that will allow me to make FDR-based directed edge inferences based on sets of time series. However, while the system should be able to make significance-based edge inferences, I have strong reservations about the ability of a VAR model to fundamentally describe the spike train data. Nevertheless, I will continue on with my exploration of G-causality based directed edge inferences.

I implemented both pairwise and conditional Granger causality methods. Here's a quick estimate of the amount of work associated with fitting the pairwise and conditional models:

Null distribution for the G-causal score:

Exponential fit appears to be decent -- I will proceed with the exponential fit for converting the test statistic (G-causal score) to a $p$-value.

Actually, on closer examination (larger number of simulations) the null distribution of the Granger score is not exponential:

Instead, I will use an empirical CCDF for the computation of $p$-value (which is what I did previously for max correlation).