Not OP, but as an example, imagine you want to fit the time series of measured monthly CO2 at Mauna Loa:

https://www.esrl.noaa.gov/gmd/ccgg/trends/

Just by looking at the graph, you can see that fitting a linear combination of a constant term, t, t2 and sin(w*t) will give you a very accurate model that has five tuning parameters (four weights and one frequency).