I found the below mentioned ARDL condition in an article which many people dont know.I asked many to comment in a forum but the members never heard about this. Any comments?
The paper reads "
However, when there are multiple cointegrating vectors ARDL Approach to cointegration cannot be applied. Hence, Johansen and Juselius(1990) approach becomes the alternative ."
Source: Autoregressive Distributed Lag (ARDL) cointegration technique: application and interpretation Emeka Nkoro1 and Aham Kelvin Uko2 . Journal of Statistical and Econometric Methods, vol.5, no.4, 2016, 63-91 ISSN: 1792-6602 (print), 1792-6939 (online) Scienpress Ltd, 2016
Well! The article from which you took the above sentences did not put any citation (source of information). Therefore, it needs rigorous sources to accept what was written in the article by Nkoro and Uko (2016). or is this the idea described in Pesaran et al. (2001)?
dear Muhammad Azam
the precondition for applying cointegration is all the variables must be non-stationary at their level form and they should be integrated(become stationary) at the same order. when is essential condition is not satisfied, we apply autoregressive distributed lag(ARDL) method.
Johansen and Juselius cointegration test is appropriate where you want to test the cointegration among more than two variables.
ARDL is an alternative to Johansen and Juselius cointegration, but not Johansen and Juselius cointegration is an anternative to ARDL.
you can also refer some standard text for this information.
any further discussion in this regard is most welcome
I don't think a reference is necessary.
If there is one cointegrating relationship and certain weak exogeneity results hold (see last paragraph below) then Engle-Granger or ARDL can provide an estimate of the cointegrating relationship. If there are two or more cointegrating relationships Johansen gives an estimate of the space spanned by the cointegrating relationships. If there are two then any two independent combinations of the two are also cointegrating vectors. It may be possible to impose conditions arising from our economic theory to identify such linear combinations.
In this case the one estimate provided by Engle-Granger or ARDL should lie in (or be "statistically" close to) the Johansen cointegration space and is therefore some linear combination of the Johansen cointegration vectors. Thus the coefficients have no structural meaning.
If you have two variable x and y and they are cointegrated and you estimate a vecm you get two equations
\Delta x = g1 ecm + lag terms of \Delta x and \Delta y +error
\Delta y = g2 ecm + lag terms of \Delta x and \Delta y +error
If g2 = 0 then y is weakly exogenous for x and one may proceed with single estimation of the x equation(Engle-Granger or ARDL).
Otherwise one can not use the single equation method even though there are only two variables and one cointegrating relationship.
Actually I have developed a model using ARDL Bounds Test approach and its perfect in all respects. Theoretically logical relationships, all tests cleared,CUSUM great, but using Granger causality and Toda Yamamoto test, I found that the Dependent Variable itself is causing some other Independent Variables and the Independents are also causing each other. How can everything go so bad when ARDL shows a beautiful story.
Pesaran, 1999 writes in his famous paper of 1999 "In this paper we propose a new approach to testing for the existence of long run relationship which is applicable irrespective of whether the underlying regressors are I(1), I(0) or MUTUALLY COINTEGRATED" Does that hint at ignoring the reverse causality test that is based on ARDL repeated equation runs with each regressor appearing as a dependent variable in the equations?
Say you have a system with four variables y, x1, x2 and x3. In a VECM x1, x2 and x3 are weakly exogenous (the error correction terms do not appear in the x1, x2, or x3 terms. In the VECM the first differences of y may or may not be significant in the first difference equations for any of x1, x2 or x3. Thus there is no contradiction in the finding of Granger Causality of y when the other variables are weakly exogenous.
The ARDL test is a test that some combination of the I(1) variables is stationary. If there are two cointegrating vectors then any combination of these is stationary. The ARDL test will find some combination of the two that is stationary by definition and will thus imply cointegration. In this case the combination that it finds can not be used for structural inference as there is no way of unraveling the two effects.
The Johansen methodology can also handle a mixture of I(0) and I(1) variables. It can also be extended to handle I(2) variables. This is indeed much more complicated than the simple ARDL tests.
I have the same question as Azam did. I also crossed that reference and the reference said clearly that when there is a reverse correlation between X and Y, ARDL cannot be applied and Johansen and Juselius is an alternative. Is there any clear suggestion for this?
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