# Johansen cointegration test and eigen vectors

#### predator21

##### New Member
Hello
I'm new to statistcs really and struggling a little to get my head around some aspects of the Johansesn test for cointegration.
I'm looking at the eigenvectors specifically, there are a number of columns, its my understanding that the ratios in the first colum result in the greatest conintegration, the second column the second best etc etc.

My question is how do I know which 'asset' to apply the hedge ratios to? I'm assuming each column shows the ratios for a different combination of thte assets, is that correct?

Or is row one always the same asset, row two always the same asset etc? If they are then is that order the same order as my input data?

#### Vin

##### New Member
Hi,

I have the exact same doubt!!

Here is where I am stuck (I am using python, just to be clear).

Trying to figure out what needs to be done after performing a Johansen's test for cointegration. Its linked to this question: https://stackoverflow.com/questions...ointegration-function-in-statsmodels/60063158. So lets say I have 4 time series on which I am doing the Johansen test, and the results indicate that we reject the null hypothesis at r <= 1, so is it correct that we have to make a linear combination of 2 variables out of the 4? We have the 4x4 eigenvector and we also have the eigenvalues list (the highest eigenvalue is for the first column of the eigenvector, right?). So, is it the first 2 rows of our 4x4 matrix that we chose to make our linear combination with the weights as explained in the quantstart article (https://www.quantstart.com/articles/Johansen-Test-for-Cointegrating-Time-Series-Analysis-in-R/)? Seems counterintuitive, as the 4 time series could have been entered in any order, right? In that case, how do we know which 2 variables to choose to make the stationary linear combination?

Please let me know if anyone has any clarifications on this or if @predator21, you were able to clear this up?

Thanks
Vin