Cointegration of a VAR(1) process

Question

I am using a Johansen procedure to test for cointegration a vectorial 4-dim vector (timeserie).

First I tested for differential stationarity of each individual vector, all of those have a unit root so we are good there.

Then I have to find the optimal number of lags as to test for cointegration using Johansen, we assume that the underlying process is a VAR process. And that's where the problem occur, I usually find K=1 (K minimizes several information criterias).

I use the package urca and the function ca.jo to run the trace and eigen tests, but ca.jo only allows K>1 (which makes sense because of the model).

What does this K=1 means ? I add that If I take K=2 both Johansen tests comes back significant and the process indeed looks cointegrated...

Answer 1

It would be the lag selection that gives the least information loss (AIC), but it doesn't necessarily mean that the true process only regress on only the first lag. Try to choose the second best K according to your information criteria. It is often found that the lag length suggested by information criteria isn't a very good fit.