I’m running some Arima()-Regressions in R with several (control-)regressors including dummy-variables and have some general questions concerning possibly cointegrated variables in Arima()-regressions. I always thought, that cointegration is a phenomenon one can only control for in (V)ECM-models. So I never checked if my variables are co-integrated, I simply checked for stationarity, took differences and ran the model. Now I just found a sentence in chapter 9.1 of the text-book by Hyndman and Athanasopoulos (https://otexts.com/fpp2/estimation.html), that one could leave the variables un-differenced, if they are cointegrated. For that I have three questions: 1. Is it harmful for my Arima()-Regressions that I differenced variables that might be co-integrated? Does this lead to somehow biased estimates? 2. How should one deal with co-integrated variables in an Arima()-Setting? Is there a possibility to include an error-correction-term as in (V)ECM-models? I’m not aware of any argument/specification in R for that. 3. How should one deal with a variable-setting, in which some variables are co-integrated (with Y_t or with other regressors) and some are not (I include up to 10 different variables including some dummy’s, so I don’t expect them all to be co-integrated)? Thank you so much in advance for any comments and help! Kind regards Stefan Schöncke
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