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.
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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.
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$\begingroup$ Thanks for your reply! I run two VARs. In the first one the variables are cointegrated. Is the autocorrelation ok in this case? In the second one some of the variables are cointegrated. What should I do in this case? Can the reason of autocorrelation be also an ommited variable? $\endgroup$– HasVarCommented Jan 21, 2018 at 22:20
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$\begingroup$ Only if your goal is building a black-boxy model for relatively accurate forecasting out of sample... However, if your goal is to understand the mechanism behind the interplay of X and Y, capturing the codependence in residuals is important. $\endgroup$– stansCommented Jan 21, 2018 at 22:23
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$\begingroup$ Actually I am going to proceed my analysis with running SVAR model with sign restrictions and then look at the impulse response functions. I guess in this case the autocorrelation is really a big problem. How can I solve it? Do I need to turn to VECM or VAR with stationary data? $\endgroup$– HasVarCommented Jan 21, 2018 at 22:34