In order for the information criteria to be able to select the model, all the models have to be estimated on the same sample. Therefore, all the models are estimated and compared using the same sample used for the model containing the largest number of lags. You can find this and other details in Lupi, C. (2009). "Unit Root CADF Testing with R", Journal of Statistical Software, 2009, 32(2), 1-19
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