I am interested in comparing a linear trend model with 1) power trend, 2) exponential trend, and 3) logarithmic trend models - comparing models using estimated AIC and BIC to identify the one that best fits my data.

I had a play with a sample dataset and wanted to make sure my models are well specified - grateful for any comment/suggestion for improvement:

clear
use http://www.stata-press.com/data/r16/friedman2.dta

* Create a time variable - rather than using the existing one (yearquarter)
g timen = _n

* Log variables
g ln_consum = log(consump)
g ln_time = log(timen)

* Linear trend model
regress consum timen
estat ic

* Exponential trend model
regress ln_consum timen
estat ic

* Power trend model
regress ln_consum ln_time
estat ic

* Logarithmic trend model
regress consum ln_time
estat ic