I know for ARIMA models in R, there is an order parameter. I want to create a diverse set of ARIMA models by modifying the p,q,and d terms. I have a for loop that applies ARIMA models to a time series in this order:
To me what is looking most exotic is the different orders of integration of your models, which you are assuming starting from 1 through 5. All asymptotic results regrading the distribution of the model parameters based on the fact that original DGP has exactly 1 as the order of integration, because most of the real life scenarios which are non-stationary in nature can be well approximated with that. Therefore perhaps usual t-values can not be justified once you cross the limit as 1.
Apart from that, in my belief you can just go ahead with different combinations of p and q parameters and choose the optimal one (based on some pre-fixed criteria like AIC/BIC or non-significance of model coefficients). However in each experiment you should fix the initial values of the time series and should keep it same for all experiment.