I read the posts, How to interpret results of Johansen Test? and How to interpret the eigenmatrix from a Johansen cointegration test? But still I am quite confused by the output. I have a project with two series: I don't reject both H0, therefore I'd say there is no cointegration.
- Test type: trace statistic, with linear trend.
- Eigenvalues (lambda):
 0.0189039550 0.0008903665
- Values of test statistic and critical values of test:
test 10pct 5pct 1pct r <= 1 | 0.39 6.50 8.18 11.65 r = 0 | 8.65 15.66 17.95 23.52
- Eigenvectors, normalised to first column (these are the cointegration relations):
Oil.l1 Fuel.l1 Oil.l1 1.000000 1.0000 Fuel.l1 -1.484484 -11.1973
- Weights W (this is the loading matrix):
Oil.l1 Fuel.l1 Oil.d -0.049059881 0.0002693549 Fuel.d 0.002111537 0.0002467205
However, I'd like to impose one. Thus, I want to read alpha and beta. From what I understand these are the vectors below the largest eigenvalue? i.e. here, beta is (1, -1.48) and alpha is (-0.049, 0.002). But, if I want to build a cointegrating relationship, then are there two of them (below), or only one (the upper one)? I believe that lower one is very unrealistic due to low eigenvalue (first one too but we impose its not):
Oil.l1 - 1.48*Fuel.l1 Oil.l1 - 11.19*Fuel.l1
Also, to get the Gamma(j) matrices for differenced data for Vector Error Correction Form, I do the following:
ECF = ca.jo(ldata, type="trace", spec="transitory", K=14) vec2var(ECF,r=1) #r = 1 for cointegration rank
According to theory there should be (p-1) matrices, i.e. 13 but I get 14. Should I simply ignore the last one?
I'd be extremely thankful for help!