Is correlation matrix of residuals , a method to check for autocorrelation of residuals in the model? I am modelling and forecasting using a factor augmented VAR. I got the following residual matrix after fitting the model. My question is how to interpret it and does it indicate any autocorrelations in the model?


This seems to be the contemporaneous correlation matrix. In a regular reduced-form VAR model, the contemporaneous correlations are allowed to be anything, so looking at the matrix you have would be irrelevant. (I am not sure what the assumptions regarding contemporaneous correlations are in a factor-augmented model, though. You may look them up in the model description.)
Meanwhile, you want your residuals to be free of autocorrelation and cross-correlation at lags other than zero. To inspect that you would run acf(cbind(e1,e2,e3)) in R. Here, e1, e2 and e3 are the residuals corresponding to the three equations.
