1. Johansen example

2. Start wingive
Load the LIBOR data base in the usual way
Start pcgive and go into the multivariate option

5. This is the basic VAR set up

6. First estimate an unrestricted VAR to test the cointegrating RANK

8. This is the results for the VAR
This is the results for the VAR. Note 3 equations the same variables in each equation

9. Now test the system for the properties of its residuals

11. Ok for tests of serial correlation but fails normality and hetero
But carry on anyway as financial data

12. Now test the cointegrating rank

15. Test of cointegrating rank
Ho r=0, probability = so reject
H0 r=1, probability = so reject
H0 r=2, probability =0.009 so reject
Strictly therefore r=3, but not sensible so conclude r=2

16. Now estimate the model subject to the reduced rank restriction that r=2

21. Estimates subject to r=2
2 cointegrating vectors (betas)
The loading weights (alpha)
Standard error of the alphas
Restricted long run matrix (PI)

22. So this is the reduced rank system where we have imposed a rank of 2.