I just performed a Johansen Co-integration test on two stocks.

The results I get are:

ans =

      r0       r1   
t1    true     false

I am using Matlab. Can someone interpret these for me?

If I have understood the test properly, they are a good correlated pair. With Mean reversion.

Are they mean reverting?

Also, I have read about stationary pairs but the technical definition is a bit confusing. If possible can someone help point me in the direction to a simpler explanation? Or may be a book to start off?

Did the test again with the following result:

>> [h,pValue,stat,cValue,mles] = jcitest(Y)

Results Summary (Test 1)

Data: Y
Effective sample size: 229
Model: H1
Lags: 0
Statistic: trace
Significance level: 0.05

r  h  stat      cValue   pValue   eigVal   
0  0  9.6981    15.4948  0.3467   0.0411  
1  0  0.0979    3.8415   0.7872   0.0004  

h =

      r0       r1   
t1    false    false

pValue =

      r0         r1     
t1    0.34672    0.78721

stat =

      r0        r1      
t1    9.6981    0.097852

cValue =

      r0        r1    
t1    15.495    3.8415

mles =

      r0              r1          
t1    [1x1 struct]    [1x1 struct]

I am trying to understand whether h=0 implies no cointegration? What exactly does the pValue tell us?

In short still trying to understand how exactly to interpret the results.

I will get onto generating the eigenvalues. And trying to understand them after this part gets clear.

I don't have the advantage of attending school at the moment and understanding this is very difficult.


1 Answer 1


Assuming you're using http://www.mathworks.com/help/econ/jcitest.html, there is 1 cointegrating relationship. The function can also output p-values.

  • $\begingroup$ I have the same problem of user31261716 in interpreting the test. What do you mean when you say only one cointegraing relationship and what can it make understanding you that? Sorry for the tricky question, but I really didn't understand. $\endgroup$
    – Quantopik
    Aug 6, 2014 at 11:40
  • 1
    $\begingroup$ Honestly, I tend to use the one in the Spatial Econometrics toolbox (its manual is a bit clearer, though there's a link at the bottom of the Matlab link I have above that provides more details). The Matlab test is testing r=0, r=1, i.e. whether the number of cointegrating relationships is some number. The test rejects r=0, so you can say there is one cointegrating relationship. $\endgroup$
    – John
    Aug 6, 2014 at 13:07
  • $\begingroup$ Hey @John thanks for the reply. I am indeed using the mathworks.com/help/econ/jcitest.html, I have changed the question a little, please have a look. $\endgroup$ Aug 6, 2014 at 13:14
  • $\begingroup$ @john possible to point me to a book or somewhere to learn in simpler terms to get started? $\endgroup$ Aug 6, 2014 at 13:19
  • $\begingroup$ @user3126171 So perhaps your problem is that you don't understand cointegration or the Johansen test, rather than necessarily how it is implemented in Matlab. As I said, the Spatial Econometrics toolbox manual is very clear about what the Johnansen test means spatial-econometrics.com/html/mbook.pdf Otherwise, most books on time series econometrics tend to cover it. You can also just google johansen test and there are many results that explain it. $\endgroup$
    – John
    Aug 6, 2014 at 14:24

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