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No matter how much I've been searching so far, I haven't found any clear explanation of the logic behind choosing the optimum version of cointegration tests (No constand, with constant, with constant and trend etc.).

Is there any formal etiology behind the intuition of such consideration?

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    $\begingroup$ Have you tried looking this up in some time series textbooks or lecture notes? Or even vignettes of relevant R packages? $\endgroup$ Commented Feb 26, 2022 at 21:23

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its about the detrend: it goes for detrending data before starting stat and eigenvalues johanson test so if you choose no const : then no trend is applied if you choose cons : a contstant dtrending will be applied and with trend : a lineaire detrending is applied . hope it answer the question . the theorie of the cointegration is very simple and complicated in the same time. simple with its principal but you have to understand the theory behind the method so you can apply them

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    $\begingroup$ I know about what the different versions of cointegration testing has to do with. My exact question is when and why should I use any of those particular specifications? What is the context? $\endgroup$ Commented Feb 19, 2019 at 10:38
  • $\begingroup$ if my brain still remember , i think that is about the long term relationship. cointegration is when a combinaison of vectors Y and X is integrated ( 0 ) this combinaison is whter with a constant or nc or cons and trend . the sufficient condition is that the combinaison is I(0) with no trend and no intercept. some case it could be I(O) with one of them or both. So for example in eviews we dont need to choose nc c o nt , but it gives result with appropriate params so we can decide with other perpective or tests like grenger's $\endgroup$ Commented Feb 19, 2019 at 15:11
  • $\begingroup$ ( if you read french this is a good example with eviews hal.archives-ouvertes.fr/cel-01771038/document ) . in my case if i work with statsmodel coint , I chose the nc so i can be sure to have a strong cointegration [ if anything seems to not having much sense ] search for long term relationship or commun stochastic trend in coointegration $\endgroup$ Commented Feb 19, 2019 at 15:12

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