Detrending data for open economy

Dear all,
I am estimating a DSGE model in an open economy. I choose to detrend the series according to EA data while the other economy is growing faster. The result is that the series of non-EA countries displays an upward trend. Is it an issue? if so, how can I solve the issue?

Yes, that is an issue as in most cases, the stationarized variables should enter the model. Differential trends therefore pose an issue. For example, import/export shares tend to grow over time in the data while the model predicts them to be stationary. It seems the literature often simply removes the “excess trends” as in e.g. Adolfson et al (2011). That is, you e.g. linearly detrend the variables. Note that HP filtering is strongly discouraged.