I am running VAR model with non-stationary time series. I am going to have a look only at impulse response functions, so I've read that I can use VAR for non-stationary time series. My model includes 4 variables. According to all ICs (AIC, HQ, SC), the lag order must be 2. But in VAR(2) model there is an autocorrelation in residuals of one variable. Is it a big problem? Can I continue my analysis with this problem? Thanks in advance.
You have to be careful when putting non-stationary processes into VAR. If the processes are not cointegrated, the estimation procedure may result in spurious regression. That is when the true coefficient is 0 but we get false significance with probability higher than the significance level.
In general, you have to explain all the serial correlation in residuals if statistical inference is the goal.