In Cointegration, adf test or for VAR models. What makes difference in having trend + Constant, Constant alone, and non.

in below link http://www.econ.uiuc.edu/~econ508/R/e-ta8_R.html

It said that My suggestion is that you run 3 different types of ADF, each of them including 1, 2, 3, and 4 lags: (i) Models with intercept and trend (int=T, trend=T) (ii) Models with intercept but without trend (int=T, trend=F) (iii) Models without intercept and without trend (int=F, trend=F)

what makes difference in choosing from 3 models how to choose


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