Thanks for your comments ondansetron. He believes that unless there is a theoretical reason for something to be true you should not model it. My guess is that someone made this point to him in the context of methods like regression (where many argue a variable should only be in a model if it makes theoretical sense) and he applies this to univariate time series.
I agree with him on those grounds, absolutely, but that depends on the context. I think prediction is different from inferential modeling. In your case, you want practical results that equate to good predictions, right? If the toenail length of the firm's CEO allowed you to accurately predict sales, no one in their right mind would argue this is causal or even a real relationship, but if it plays out well in real life, you will probably use it based on its performance.
While authors disagree I think this concern is generally less in univariate time series, be it ESM or ARIMA, which simply models what has occurred and assumes that it will continue (because it assumes there is a unknown generation process that generates the results and these will not change). He is not the easiest person to discuss things with, it ends up being confrontational and I am not good at confrontation.
Thanks for your comments. I would argue the same thing in honesty.
I think you can approach it from the aspect that you both agree the common goal is a high performing model in the sense of accurate predictions. Seasonality may be a proxy in some way or capturing some other underlying process, but if it leads to good out of sample predictions, why change unless discarding seasonality results in better predictions. If you want to make inferences about the relationships with the DV, then I agree to remove something without substantial justification beyond a significant p-value.
One thing I forgot to ask. If you are modeling monthly data (including seasonality) is it an issue if you don't have complete sets of 12? I have 49 months (not exactly 48). I have never seen suggestions if this matters to model time series, just that you would want at least 48 points.
I don't think it matters to be honest. Whatever the seasonality is (4 periods, 12, etc.) each observation will have an indicator for which "season" it is, if I remember correctly. If I seem off point, please give me an example of what your model might look like.