I have a novice background in time series (some ARIMA estimation/forecasting) and am facing a problem I don't fully understand. Any help would be greatly appreciated.
I am analyzing multiple time series, all over the same time interval and all of the same frequency, all describing a similar type of data. Each series is just one variable, there are no other corresponding predictors that I'm looking at.
I have been asked to estimate a single model that describes ALL the series - for example, imagine I could find one ARIMA (p,d,q) with the same orders, coefficients, etc. that could fit all the series. My supervisor does not want me to separately estimate each series, nor does he want me to do some sort of VAR model with dependencies between the series.
My question is: what would I even call such a model, and how might I go about estimating / forecasting it? If it's easier for you to use code examples, I speak both SAS and R.