Johansen cointegration test: interpret the result I am trying to develop a stationary time series with 6 variables in Matlab. Can anyone tell me whether the 6 variables are cointegrated? The results I got are:

 A: When examining the table you should go down row by row comparing the test statistic to the critical value, and see when you cannot reject the null hypothesis for the first time, for a chosen significance level. That will show whether the series are cointegrated and what the cointegration rank is. 


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*If you cannot reject rank<=0, the series are integrated but not cointegrated. 

*If you reject all the cases including the maximum rank (here rank<=6), the series are not integrated to begin with (and hence there is no cointegration).

*If you reject rank<=0 but stop before or at the maximum rank, the series are integrated and cointegrated, and the cointegration rank is the one at which you stopped (could not reject).


For example, choose 5% significance level. Then the first non-rejection when using the trace statistic is at r<=3, and the same is true for the eigenvalue statistic. Hence, you do not reject the null hypothesis that the data is cointegrated and the cointegration rank is 3.
