I have 1200 data points and I'm building 6 different time series models. One with 1200 data, another model with 1100, 1000,..., 700 and then I would choose the best model but I don't know how to select between different data lengths. I'm doing so because my data have time based trend and I don't know how many data should I use to make the models.
I've tried to use $$AIC=-2\log(L)+2k$$
where $k$ = # of Parameters, $L$ = Likelihood, $N$ = Data Length
To avoid AIC always selecting the model with minimal data length, I've used the logarithm in the base N, but it still prefers to choose the model with lower N.