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I am using regression with ARIMA error which modifies the error terms to generate correct results for time series regression. I know that if two variables have a trend in it then you may get spurious regression unless the variables are co integrated. However, every discussion I have run into about this proceeds into error correction models or var models which are very difficult to interpret/run to me. I was wondering if it was valid to use regression with ARIMA error if there are trends in the variables (no discussion of this method I have found answers this).

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  • $\begingroup$ One issue that I suspect is pertinent to this, although I am not sure is that I think each variable in regression with arima error has to be integrated of the same order. Can you analyze data at all with this method if the variables are integrated of another order from each other? $\endgroup$
    – user54285
    Commented Jul 20, 2020 at 22:28
  • $\begingroup$ This stats.stackexchange.com/questions/478080/spurious-regression suggests a basic issue that drives my questions. "Notice that this is equivalent to differencing both yt and xt before fitting the model with ARMA errors. In fact, it is necessary to difference all variables first as estimation of a model with non-stationary errors is not consistent and can lead to “spurious regression”. To me this suggests you can not use regression with ARIMA error if your Y and X are integrated of different orders, but I am not sure this is the case - I have never found this said. $\endgroup$
    – user54285
    Commented Jul 21, 2020 at 14:21

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