Statsmodels VAR plot_acorr() amount of plots

Question

I am working on a statsmodels VAR model to forecast some values and want to analyze the created model. In the examples and in some books I read about calculating the autocorrelation of the residuals to see whether the assumptions made are valid or if information is missing. I used the plot_acorr function of the VARResults class but noticed that it produces a $k\times k$ plot of autocorrelations given $k$ variables. Since autocorrelation is the correlation of a signal with lagged values of itself, I would assume that only $k$ autocorrelations are possible. What exactly are the other autocorrelation graphs?

Answer 1

I do not use Python, but here is what I think may be going on. If the VAR model is indeed a statistically adequate model for the conditional mean of a vector-valued time series, conditioning on its past, then the errors should not only have zero autocorrelation for each individual component time series but also zero lagged cross correlations across the components. That is why you would inspect a $k\times k$ matrix of auto- and lagged cross-correlation functions rather than just the $k$ autocorrelation functions.