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I am not quite sure if I understood your question. Considering something as significant is completely subjective and any rule regarding that should be finalized before starting any experiment. Are you looking for something on what is the sampling distribution for the estimates corresponding to the V...

Hi Wedira, you are done completely correct. As you said correctly to determine the optimal lag length, you need not make data stationary. This is because here you are not estimating the model coefficients. Non-stationarity matters in deriving the asymptotic properties (i.e. distribution, consistency...

If I strictly follow the definition of co-integration, there cant be anything like that.

In your system you have variables with maximum order of integration 1. Therefore it is an I(1) system. And as you have 1 stationary variable there is trivially one cointegration relationship i.e. trivially rank of the cointegration matrix is minimum 1. However this rank can be max. of 2 depending on...