Professor Olasehinde Timilehin commented about the ARDL as........
1) ARDL can incorporate variables of I(0) series wholly but there is no room for cointegration testing but error correction representation is highly and always permissible. 2) ARDL can incorporate variables of I(1) series wholly but some conditions are attached. i: using pesaran bound test, if cointegration exist among the variables, run the model in level and error correction representation is highly and always permissible ii: If cointegration do not exist among the variables, run your model in First difference ; error correction representation is highly and always permissible. 3)This is the most controversial aspect of the exposure. This section seek to find answers to i: what should be the nature of the dependent variables? ii: Can I(1) and I(0) series be cointegrated always or conditionally? The first argument is that, your dependent variable must be I(1) in nature and there must be atleast one I(1) regressors in order for possible cointegration to exist , for valid error correction form to exist and for valid inferences to exist. Pesaran failed to give full direction about this and had been silent on this for years ,but the theory behind cointegration never remained silent ..i need to show you this proof Y(t) = a + b*X1(t) + c*X2(t) + d*X3(t) + e(t)Y(t) > (1)X1(t) > (1)X2(t) > (0)X3(t) > (0)here the linear combination of Y(t) and X1(t) called it Z(t)=k*Y(t) + w*X1(t) , if cointegrated will be I(0) then the combination of Z(t) and the other regressors (X2(t) and X3(t)) will be I(0)......i.e e(t) = f*Z(t) + c*X2(t) + d*X2(t) will be I(0).....I suggest two steps method in spirit of lutkepohl and kraitzig by first testing for cointegration between /among the I(1) variables and if it exists, theoretically, this must also combine with the I(0) series to be cointegrated. Moreover, you have to know that, there are some reports you have to give about ARDL model that failing to do so render your report useless. These are the dynamic nature of the ARDL result; mean lag, median lag and the dynamic elasticity/multiplier both interim and cumulative( confidence interval may be of interest in order to know the significant and insignificant region) .Due to time and space limitation, this is what I could gathered this morning,more will be added at my leisure time...and please I am liable for any typos made in the write up ....happy New season.
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