I have two time-series a & b. The objective is to find out whether two series are cointegrated or not. I am using Johansen Test in R to find this out.
I am using urca package of R.
Here is the summary of test (trace test with constant intercept): ca.jo(cbind(a,b), type="trace", ecdet = "const", K = 2, spec ="longrun")
Test type: trace statistic , without linear trend and constant in cointegration
 1.729720e-02 4.118294e-03 1.294090e-19
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct r <= 1 | 2.46 7.52 9.24 12.97 r = 0 | 12.88 17.85 19.96 24.60
Eigenvectors, normalised to first column: (These are the cointegration relations)
a.l2 b.l2 constant a.l2 1.000000 1.0000000 1.000000 b.l2 -3.662895 0.6463026 1.725186
constant 1135.666923 -2889.4155208 -7862.128714
Weights W: (This is the loading matrix)
a.l2 b.l2 constant a.d 0.002621493 -0.006226421 1.245608e-18 b.d 0.010169925 -0.001446919 2.187151e-18
Now my question how to interpret this result and determine whether a & b are cointegrated or not? What is a loading matrix in a cointegration test? How to interpret the critical values? How to determine whether to keep a constant intercept or zero intercept? Do I need to check individual series is an I(1) series before running johansen test?
There is a similar question which has been asked before here but it didn't answer my question completely.