I need some help understanding the results of Johansen Cointegration test run on MATLAB. I am quite new to econometrics and do not fully comprehend what MATLAB has come up with. I would be really in debt if someone could explain the following in layman terms.

The test was run on two series.

Data: Y
Effective sample size: 1871
Model: H1
Lags: 0
Statistic: trace
Significance level: 0.05

r  h  stat      cValue   pValue   eigVal   
0  0  11.0750   15.4948  0.2115   0.0037  
1  1  4.2114    3.8415   0.0402   0.0022  

h =

      r0       r1   
t1    false    true 

pValue =

      r0         r1      
t1    0.21149    0.040163

1 Answer 1


The test fails to reject the null hypothesis of no cointegration since the p-value for r0 is greater than 0.10, and, instead, it rejects the null hypothesis of 1° rank cointegration r1 at 5.0 % level of significance (since the p-value is 4.01 %).

So, looking at the test results, the series are not cointegrated, although I suggest to check for higher ranks and level of cointegration (r2, r3,...).

You can find more references about the test on mathworks and on the quant.stackexchange site about the Johansen interpretation test in R.

  • $\begingroup$ Hi Quantopic, I did a little reading on Johansen's test. correct me if i am wrong, but shouldn't we compare the stat value with cvalue? $\endgroup$
    – cryptex
    Apr 19, 2015 at 18:33
  • $\begingroup$ Yes you're right @cryptex. This quant.stackexchange.com/questions/3526/… question is an example of what you commented about (even if it is in R and not in MATLAB). Looking at the p-values as to the stats is the same thing anyway. $\endgroup$
    – Quantopik
    Apr 20, 2015 at 0:57
  • $\begingroup$ @cryptex if the answer has been helpful, please consider the possibility to check the question as answered or upvote. $\endgroup$
    – Quantopik
    Apr 20, 2015 at 10:25

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