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I am trying to see if house price is cointegrated with interest rate, per capita income and rental vacancy rate and got the following output from ca.jo in R:

# Johansen-Procedure # 
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Test type: maximal eigenvalue statistic (lambda max) , with linear trend 

Eigenvalues (lambda):
[1] 0.52471580 0.12579545 0.10395269 0.06262468

Values of teststatistic and critical values of test:

          test 10pct  5pct  1pct

r <= 3 |  8.47  6.50  8.18 11.65

r <= 2 | 14.38 12.91 14.90 19.19

r <= 1 | 17.61 18.90 21.07 25.75

r = 0  | 97.44 24.78 27.14 32.14

Eigenvectors, normalised to first column:
(These are the cointegration relations)

                    y.l2   income.l2 interest.l2     vac.l2
y.l2             1.00000000  1.00000000   1.0000000 1.00000000

income.l2   -10.16285869 -1.32443038 -12.6597547 0.61669614

interest.l2  -0.06759846 -0.35179735  -0.1535533 0.02143767

vac.l2        0.22771577  0.02087503  -0.4814448 0.02113804

So from what I understand, the output indicates that there is one cointegration relation. And using the 1st eigenvector, I should get that y(which is log_price)=-10.16*income-0.0675*interest+0.227*vacancy rate. However, I ran a ADF test on this combination and got p-value 0.11 (meaning the combination is still non-stationary!). Why is that? Am I using the wrong thing? What does the ".12" mean after the variable names?

Thank you for any help!

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  • $\begingroup$ Is your interest rates series I(1)? $\endgroup$ – tagoma May 18 '13 at 11:36
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Maybe you have made some misspecification with regards to deterministic terms or lag length. Try to estimate a restricted VECM from your ca.jo()-output with cajorls(), extract $\beta$ and run the ADT-test on that process.

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