Johansen Cointegration test issue

#1
Hello,

Let me describe the issue: I have a vector of four time series, each component of which is I(1). When I put the four series into a matrix and run the Johansen cointegration test, the library I am using reports that the rank of the error correction matrix is four. If my understandingis correct, this would mean that each of the four input time series must be stationary.However, tests(Augmented Dickey-Fuller, KPSS) pointed to each of the input series being I(1). Can anyone provide some insight into what may be happening? Also, if I accept that the rank of the error correction matrix is four, and use the four generated error correction variables in a VAR in first differences, three turn out to be significant(the regression itself is good, p-value of F-statistic very small, Durbin-Watson close to 2).

Thank you in advance.