# cointegration - Johansen test - how to build a model and calculate a half life of the mean reverting spread?

I have got two time series on which I have run the Johansen test for cointegration in R (package: urca). From the results I can see that no series is mean reverting and there is the cointegration at r=0 at 90% confidence level (is that correct interpretation?)

Using the results I want to build a model

$$y_{1t}=β_2 \ \mathbf{y_{2t}} + u_t, \quad \quad where \ \ \ u_t∼I(0) \quad \quad (12.4)$$ $$\mathbf{y_{2t}}=y_{2t-1}+vt, \quad \quad where \ \ \ v_t∼I(0) \quad \quad (12.5)$$ as presented here http://faculty.washington.edu/ezivot/econ584/notes/cointegration.pdf p.435

I assume that the $u_t$ can be seen as the modeled difference between series (spread). How could I calculate the half life of the spread. Should it be log(2)/Eigenvalue as suggested in the comment to this question? https://quant.stackexchange.com/questions/2076/how-to-interpret-the-eigenmatrix-from-a-johansen-cointegration-test

Which number from the below example should be taken to calculate half life?
What number should be taken for $\beta_2$?

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

Test type: maximal eigenvalue statistic (lambda max) , with linear trend

Eigenvalues (lambda):
 0.00308977956 0.00008189485

Values of teststatistic and critical values of test:

test 10pct  5pct  1pct
r <= 1 |  0.37  6.50  8.18 11.65
r = 0  | 13.82 12.91 14.90 19.19

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

A.l2     B.l2
A.l2  1.0000000 1.00000000
B.l2 -0.8064909 0.00237543

Weights W: