I've been learning X12-ARIMA by looking at data from a friend's service company, and wondering how to model the capacity of the company. That is, if the company is limited by a particular resource to only be able to handle 1,000 customers a week, how do I keep my ARIMA model from happily predicting 1,200 customers next summer?
(This isn't an issue with time series like GDP or stock prices, which don't have a hard cap.)
It doesn't seem that you can do anything in the optimization phase (which is simply choosing parameters), nor with exogenous variables (which drive the process, not react to it). Maybe changing the ARIMA model to a State Space representation would help? (Any recommendations on an R package to do this? I've looked at several and DLM's many matrices confuse me at this point.)