If all my dependent and independent variables are stationary at first difference NOT at level, SHOULD I REPLACE (ardl y x1 x2) with (ardl d.y d.x1 d.x2)? when there is no cointegration and I want to estimate a short-run ardl model or it doesn't matter?, since my diagnostic tests are good enough to rely on when running (ardl y x1 x2)OR these diagnostic tests are invalid as well?
Thanks in advance.
https://blog.eviews.com/2017/05/autoregressive-distributed-lag-ardl.html
Yasmine El-Hady
If all dependent and independent variables are stationary at first difference, use the ARDL model with first differenced variables (ardl d.y d.x1 d.x2). Since your variables are stationary at first difference, the ARDL model assumes they are integrated and cointegrated at order 1, I(1).
If you apply the ARDL model with the original level variables (ardl y x1 x2), you risk erroneous regression or long-run non-stationarity. This may lead to erroneous coefficient estimations and incorrect model interpretation. Thus, you must specify the ARDL model correctly (ardl d.y d.x1 d.x2) because the ARDL model is designed to capture the short-run relationship between non-stationary variables.
Diagnostic tests, independent of specification, reveal model quality. Therefore, always perform diagnostic tests to verify the ARDL model's assumptions and reliability. Stability, residual, and model selection criteria diagnostic tests are among other test options at your disposal.
Therefore, even though your variables are stationary at first differences, you should still use the first differences of your variables to estimate the ARDL model. This specification will help you avoid any potential problems of spurious regression and ensure that your results are reliable.
Dickson Utonga
Thank you for the clarification.
But, should this also apply for the Granger causality Wald test? Should it also be applied at the first difference? after running a VAR model including the first difference for each variable.
Yasmine El-Hady Yes, when using the Granger causality Wald test after running a VAR model that includes the first difference for each variable, you should apply the test at the first difference level. This is because you have already differenced all the variables, and therefore the causality relationships that you are testing are at the first difference level. If you try to apply the test at the level of the original variables, the results may be misleading or incorrect. Therefore, it is important to apply the test at the appropriate level, which in this case is the first difference level.
Dickson Utonga
Thank you very much for the clarification, MR. Dickson
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