Let's say I have an MA(4) model, and I find that theta 4's 95% confidence interval contains 0. Thus, I set theta 4 to 0, and now my AICc decreased. Can I call my new model an MA(3)?
Iterate to a minimally sufficient model incorporating as necessary ARMA structure and deterministic structure. . How to evaluate deterministic vs stochastic components of a time series? . In my experience if you have unnecessary AR structure this will often (always !) inject cancelling MA structure. It is indeed my suggestion to eliminate any and all unwarranted structure in any model as Einstein once said .. models should be as simple as possible BUT not too simple..
Since some software doesn't have the feature to automatically simplify they recommend that you don't simplify because the software doesn't simplify.