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hi, i am doing johansen cointegration procedure on several different series, but i have encountered some problems, and i just wanted to double-check here if anyone knows the answer. i appreciate any help.

1. in determining the order of integration of each series, in doing the augmented dickey-fuller test, i conclude that some series has the specification of a random walk + drift + deterministic trend, therefore differencing alone won't make it stationary, but i also have to de-trend. what does this mean for the order of integration? is the series considered I(1), or not, since differencing alone won't make it stationary [however, when i did do the ADF test on some of these series, the first difference was stationary, so maybe the deterministic part is not so strong, i don't know?]

2. second, in selecting the lag length, even after 10 lags i find that there is serial correlation after lags 10. is this ok, or should i select even higher? for my model, from experimenting, it seems i have to go up to 13 lags to remove all serial correlation for 20 lagged values of each series- is 13 lags too much, or should i just use 10?

thank you for any help, apologies if my questions are simple, i just felt a bit stuck,

question: while running johansen coint test on two price series, I found I series is stationary at first difference, another is stationary at second difference. I have done cointegration test on level values of first series and first differenced values of second series. is this right??