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If there are two I(1) series that are not cointegrated, why could it be that if I create a VECM and impose restrictions implying that they are cointegrated, that I cannot reject this restriction according to the LR test? Could this be a spurious result, or generally how could I explain this theoretically?

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  • $\begingroup$ What do you mean? Could you be more specific? What kind of restrictions? For example, if you impose a coefficient value rather than estimating it, there is no point in testing its significance as the value is not estimated but imposed. $\endgroup$ – Richard Hardy Apr 16 '16 at 14:52
  • $\begingroup$ For example, if D(Y)=C+B(1)D(Y(-1))+B(2)D(X(-1))+A(B(3)D(Y(-1)+B(4)D(X(-1)) where C is a constant, A is the speed of adjustment and the B's are coefficients. Then I imposed that B(3)=1 and B(4)=-1 however the results LR stat implies that this restriction is infact valid. That's why i'm confused? $\endgroup$ – Vladmir Putin Apr 16 '16 at 15:01
  • $\begingroup$ in other words, given that the imposed restriction is valid, what does that say about the cointegrating relationship? $\endgroup$ – Vladmir Putin Apr 16 '16 at 15:08
  • $\begingroup$ What kind of LR stat do you have in mind? Do you test the model with restriction against the unrestricted model and get that the restrictions cannot be rejected? Another issue could be that the LR statistic may have an unusual distribution in presence of integrated time series. Are you sure you are comparing your test statistics to the correct critical values (correct null distribution)? $\endgroup$ – Richard Hardy Apr 16 '16 at 15:09
  • $\begingroup$ Basically, from what i've been told, when you impose the restriction, the software automatically tests the restricted model against the unrestricted model. Hence, the null-hypothesis is that the restrictions are binding but the p-value obtained is 0.97 so we cannot reject the null hypothesis. $\endgroup$ – Vladmir Putin Apr 16 '16 at 15:12
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You are testing whether restrictions within a VECM hold, which is not directly related to testing for cointegration. These are two different things. If the series are not cointegrated, you are comparing one inappropriate model to another inappropriate model, and the test result tells you that there is little difference between these two models. But it does not tell you that there is cointegration.

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