VAR nonstationary series

I have a question. If some series are nonstationary, is it still reasonable to include them into a VAR model? If not, how can I solve it? I do not want to try 1st difference. Thanks a lot!

That is a quite complicated topic. First, you need to take a stand on whether the nonstationarity comes from a deterministic or a stochastic trend. If it is the former, you should add a trend to the VAR. If it is the latter, there is the matter of whether there is cointegration between the series. In that case, you can still estimate the VAR with the non-stationary series. A reference here is Sims/Stock/Watson (1990), Econometrica.

Thanks for your helpful advice!!