# Johansen-Procedure: Values of teststatistic and critical values of test?

I am trying to run a Johansen-Procedure in a set of macroeconomic variables (GDP, credit outstanding and industrial production). I am working with them in level.

How should I interpret the following result? Which "r" should I use next to run the model?

######################
# Johansen-Procedure #
######################

Test type: maximal eigenvalue statistic (lambda max) , without linear trend and constant in cointegration

Eigenvalues (lambda):
  6.999273e-01  3.188663e-01  1.303763e-01  5.099467e-02 -6.157574e-17

Values of teststatistic and critical values of test:

test 10pct  5pct  1pct
r <= 3 |  3.04  7.52  9.24 12.97
r <= 2 |  8.10 13.75 15.67 20.20
r <= 1 | 22.27 19.77 22.00 26.81
r = 0  | 69.82 25.56 28.14 33.24

[...]


My goal is to estimate the best VEC model so I can forecast those variables. I choose the number of lags from the VARselect function (saved as def), AIC(n) criteria, and then run a vec model.

jo.eigen <- ca.jo(training, type='eigen', K=def\$selection,
ecdet='const',
spec='transitory',
season=4)

vec <- cajorls(jo.eigen, r= ???)
vec.level <- vec2var(jo.eigen, r= ???)


Thank you very much!

The maximum eigenvalue test is used to determine the rank of the coefficient matrix associated with the cointegration term. It is a sequential test starting from the hypothesis $$H_0: r=0 \\ H_1: r=1.$$ The test statistic at r=0 is 69.82 and the 1% critical value is 33.24, meaning we reject $$H_0$$. Now we test $$H_0: r=1 \\ H_1: r=2.$$ Now the test statistic is rejected at the 5% level, but not at the 1% level. If you find this threshold 'acceptable' you move on to $$H_0: r=2 \\ H_1: r=3.$$ Here the test breaks down, we cannot reject $$H_0$$ at any of the typically used significant levels (1%, 5%, or 10%), and accept r=2.