I am comparing a random forest model to a GLS model using a univariate time series that has a deterministic linear trend. I am going to add a linear time trend covariate (among other predictors) to the GLS model to account for the changing trend. To be consistent in my comparison, I was hoping to add this predictor to the random forest regression model as well. I have been looking for literature on this subject and can't find much.
Does anyone know if adding this type of predictor is inappropriate in a random forest regression for any reason? The random forest regression already includes time-lagged variables to account for autocorrelation.