# matlab interpretation of johansen cointegration test

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


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,...).