# Impulse response for cointegrated variables

I know that VAR should be employed only with stationary series. Is the same condition required for analysing impulse response? That is, should the impulse response be analysed on stationary variables only?

Because normally a VAR is estimated using stationary variables and after that impulse response can be analysed. But if our variables are cointegrated, then we proceed with estimating restricted VAR which is VECM. When I observed the impulse response after estimating VECM, I found that impulse response was shown for nonstationary variables.

• Let me inform you that if the answer solves your problem, you may accept the answer by clicking on the tick mark to the left of it. On the other hand, if something is still unclear, you may ask in the comments. – Richard Hardy Apr 20 '17 at 11:31

## 1 Answer

It is fine to analyze impulse-responses for stationary or nonstationary variables as long as the model is well specified, enabling sensible impulse-response analysis. For example, you may analyze impulse-responses for a VEC model as long as it adequately describes the system of time series under consideration.

• Please throw some light on the lag length criteria. For example if we have estimated the VEC at 10 lags as defined by AIC (because Johansen cointegration is sensitive to lag selection), and as impulse response in VEC does not provide insight about statistical significance, do we have to choose the same lag length for estimating VAR as VAR provides statistical significance while looking at impulse response particularly in Eviews. – khalid ulislam Mar 31 '17 at 10:48
• @khalidulislam, this is a separate question and should be posted as such. But let me know if you need any clarification for the original question. – Richard Hardy Mar 31 '17 at 11:22
• How will a VAR of nonstationary variables well specified when VAR assumes stationarity of variables? The basic purpose of VAR estimation is to estimate the long-run relationship, however stationarity condition can be fulfilled by taking first difference of the variables. But, if the purpose is to estimate the long-run relationship between variables which are not cointegrated is VAR applicable while using non-stationary variables? – khalid ulislam Apr 1 '17 at 13:45
• @khalidulislam, You have noted yourself that under cointegration, a VAR model can be represented as a VECM, and there you can see both the short-run effects (the lag terms) and the effects due to the long-run relationship (the error correction term). If you like, you can represent it as VAR with some restrictions on coefficients. – Richard Hardy Apr 3 '17 at 8:10