I create a demand forecast for a company that sells, say, toasters. We have one old standby model that's just finally stocked out, and a series of much newer models with shorter time series of sales to work with.
Our historic forecasting method (in R) was a much more complicated version of this:
fit <- Arima(old_standby) refit <- Arima(shiny_new_model, model = fit) new_model_future <- forecast(refit, h = 60)
This was all well and good until two things happened. First, we stopped selling the old standby, so we don't have any recent data on that. Not necessarily a problem - as long as sales for the old standby in the past look like sales for new models now, it shouldn't screw things up.
The second issue is the problem though. We also gave out 1-week coupons for our new models that caused a massive temporary spike in sales. Usually, I'd incorporate these as additional regressors in the
Arima, but I can't do it because we had already stocked out of the old standby at that point.
Is there any way to fit an Arima to the data for the old standby, refit it to the data for the new model (incorporating a dummy regressor for the coupon), and then predict? Something like this:
fit <- Arima(old_standby) refit <- Arima(shiny_new_model, model = fit, xreg = coupon_dummy) new_model_future <- forecast(refit, h = 60, xreg = new_coupons)
I'm guessing the answer is "no," because you can't fit the auto-regressive portion of the model against two different sets of data at the same time. But I still thought it was worth asking if anybody had any ideas.