I've been trying for hours to figure this out on my own. Unfortunately, it's not working very well, so I decided to come here for help. Other responses to similar questions didn't quite answer my question.
I'm supposed to interpret data from a Johansen test in R. Here is the output:
x = cbind(rt3,rt6) y=data.frame(x) cot=ca.jo(y,ecdet="const", type="trace", K=3, spec="transitory") summary(cot) Eigenvalues (lambda):  1.045e-01 7.896e-03 1.38e-18 Values of teststatistic and critical values of test: test 10pct 5pct 1pct r <= 1 | 4.64 7.52 9.24 12.97 r = 0 | 69.17 17.85 19.96 24.60 Eigenvectors, normalised to first column: (These are the cointegration relations) rt3.11 rt6.11 constant rt3.11 1.0000 1.0000 1.00000 rt6.11 -0.988 -5.933 0.04384 constant 0.1343 26.991 33.9232 Weights W: (This is the loading matrix) rt3.11 rt6.11 constant rt3.d -0.177 0.00271 8.38e-19 rt6.d 0.1066 0.00263 -9.04e-19 mcr = cajorls(cot) mcr $r1m Call: lm(formula = substitute(form1, data = data.mat) Coefficients: rt3.d rt6.d ect1 -0.177 0.1066 rt3.d11 -0.011 0.1208 rt6.d11 0.174 0.0693 rt3.d12 0.014 -0.0263 rt6.d12 -0.095 -0.0803 $beta ect1 rt3.11 1.0000 rt6.11 -0.988 constant 0.1344
What I'm trying to do is to use this information to write the VECM formula based on this data.
I believe that the loading matrix would be alpha, and that beta is the cointegrating vector (1, -0.988).
I'm having trouble realizing how to put the eigenvector matrix into use, that states the cointegration relations. I see that the beta vector is a part of that matrix.
Then I get the coefficients following the cajorls. I realize that d11 d12 must mean t-1 and t-2 lags, but I'm still not quite sure what to do with this and how to plug these coefficients properly into the VECM model.
I've tried and thought, I've read Dr. Tsay multiple times, searched online. But basically I just can't seem to figure out what to do.
TLDR version: I'd appreciate help to put this information to create a VECM formula.