What is Johansen test?

The Johansen test (Johansen, 1988, 1991) estimates the VECM by maximum likelihood under the restriction $\operatorname{rank}\Pi = r$: after removing the short-run dynamics from $\Delta Y_t$ and $Y_{t-1}$, the squared canonical correlations $\hat\lambda_1 \ge \dots \ge \hat\lambda_k$ between the two residual sets give the trace statistic $-T\sum_{i>r}\ln(1 - \hat\lambda_i)$ for rank at most $r$, and the maximum-eigenvalue statistic $-T\ln(1 - \hat\lambda_{r+1})$; the corresponding eigenvectors estimate $\beta$.