I am studying on VECM models of some stock prices. Need some clarification on the interpretation of this output of EViews. The report shows that "None" is not being rejected and "at most one" is being rejected at CI=95%. What should I assume? Cointegration or no cointegration? There are two variables in the model.
Dear Abhishek, you just answered your question:
1. "The report shows that "None" is not being rejected " - you could not reject "no cointegration" (In other words, your null hypothesis is "no cointegration" and you failed to reject it/you accept it, meaning that there is no cointegration).
2. " and "at most one" is being rejected" - you rejected that there is at most 1 cointegration vector (In other words, you rejected the alternative hypothesis that there is a maximum 1 cointegration vector, meaning that there is no maximum 1 cointegration vector).
In short, you don't have a cointegration relationship according to both Trace and Eigenvalue tests.
None indicates that there is no co integration. None is not rejected means that there is no cointegration among the variables. But at most 1 is rejected. So there is maximum of one co integration among the variables is rejected. So there is no cointegration in the given study.
The reported results shows that there is no cointegration among the variables.
When the probability (p-value) is higher than 0.05 you cannot reject the null hypothesis, and you conclude that there is no cointegration between the studied variables. If the p-value is less than 0.05, you reject the null hypothesis and accept H1: variables are cointegrated
Null Hypothesis: no cointegrating equation
Alternative Hypothesis: Null hypothesis is true
Make your rejection of the null hypothesis at the 5% level
Dear Abhishek Wagh ,sorry to say that, i am not agree with all the answers given before me ...Because, Johansen co-integration test is based on the sequencing of the tests to determine the rank of the matrix which means if the null hypothesis of first test is not rejected, sequencing of test stops there and if null hypothesis is rejected, we move to next test. Can be explained in easy manner as follows:
for Maximum Eigen test (for example)
1) H0 : r=0 and H1 : r=1
If null hypothesis is not rejected, the sequence stops here. we say that r=0
If null hypothesis is rejected, then we move to 2nd test given below
2) H0 : r is equal to 1 or less than 1 and H1 : r=2
If null hypothesis is not rejected, the sequence stops here. we say that r=0
If null hypothesis is rejected, then we move to 3rd test given below
3) H0 : r is equal to 2 or less than 2 and H1 : r=3
If null hypothesis is not rejected, the sequence stops here. we say that r=0
If null hypothesis is rejected, then we move to 3rd test and so on
Hence, from your results of Johansen test, it is clearly visible that
1) H0 : r=0 and H1 : r=1 , the null hypothesis is not rejected, so the sequencing of test stops there. and r=0 means there is no cointegrating relationship exists there.
No need to think of At Most 1 Hypothesis.
Thank you.
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