Why the Federal Funds rate isn't detrended in a VAR model? In FAVAR (factor augmented VAR) paper (https://faculty.wcas.northwestern.edu/~lchrist/finc520/QJE.pdf), the following transformation code is applied to the data:
1—no transformation; 2—first difference;
4 —logarithm; 5—first difference of logarithm.
There is no transformation for the federal funds rate, among several others. The paper does not say why, but is it because these series are already stationary in levels? Would it hurt to detrend them even if they are stationary in levels?
Yes, if the series is already stationary then there is no need to difference the data to remove a trend. In fact, there is a cost associated with unnecessarily differencing the data such that you are removing / losing relevant information. More generally this is related to the concept of cointegration where even if series are non-stationary, if they are co-trending then you lose more information by differencing than by including the lagged levels in the model specification.
You might also find the following question and answers helpful for thinking about this in a slightly different context: https://stats.stackexchange.com/questions/415914/is-it-a-valid-claim-that-by-differencing-a-time-series-it-loses-its-memory-an