Here's the scenario:
- I have many different time series I would like to forecast
- I've been through the process of making a seasonal ARIMA model for many of the time series just as part of exploration
- Each of the time series also have a set of static (read: do not change over time, but vary by series) variables associated with them (could be continuous or categorical)
- I would like to be able to build a system to forecast each time series incorporating the static variable
Oversimplified example: I have the daily sales of kool aid over the past decade and can slice the information into the five different flavors in both a sugar-free and sugar-full varieties. Is there a way to create one model that handles the different combinations above and the seasonal/AR/MA characteristics of each product?
My immediate thoughts:
- Slice the time series to generate a mutually exclusive, collectively exhaustive set of time series and forecast each one using standard methods (seems less than optimal).
- I suppose that if the impact of any static variable is roughly constant regardless of timing then I could just create a multiple regression model using all the data and ignoring date/time, so this question may be more about the interaction of the static variables and the internal components of the time series.
Any ideas? Let me know if there's a name for this and I'm just searching ineffectively.