Time series forecasting: How can I adjust my forecast to incorporate external predictions at a different time scale?

Question

I have information about past and future values that I want to incorporate into my timeseries model (experimenting with ARIMA and other models) in order to predict the future at a more granular timescale. I'm struggling with how to include it.

For example: I want to forecast ice cream sales at my store, weekly, for the next year, and I have weekly data for the last couple of years. I know the % growth for the past couple of years on an annual basis (say, 2%, 3% and 3.5% for the last three years), and I predict the coming year's growth to be 6%.

Assuming I'm pretty confident in my prediction of 6% growth for the coming year (maybe I plan to ramp up advertising throughout the year etc. but can't really say for sure that the 2%, 3%, and 3.5% in the past were entirely due to advertising), I want to incorporate this information (but, I'm not very good at predicting growth on a weekly basis so I don't have weekly growth predictions).

But, including growth as an external regressor doesn't seem to make sense, because (past) growth isn't a separate factor/regressor - it's just the last three years of weekly data (that are already in the model) presented on an annual basis.

Assuming I still want to incorporate the information from my model (growth patterns within a year, high seasonality in ice cream sales), should I just manually adjust the forecast after creating it to force next year's total to equal 6% growth? If so, is there a canonical way to do this? For example, if I calculate that my model forecasted 4% annual growth for the coming year, I could just add a small percentage to each week to make up the difference between the 4% the model forecasts the 6% I predict myself. I would also need to consider how to distribute those small percentages across weeks, as annual growth likely doesn't abruptly change from 3.5% to 6% on the first day of the coming year.

Answer 1

I can suggest a simple approach. Extract the trend, seasonality and noise from the series using any number of available methods.

When you forecast, if you're confident in your trend forecast, then use your own expert outlook. Next, you add back the seasonality. The remainder, a noise, can be regressed on exogenous variables if you have forecasts for them. Otherwise, in forecasting you can drop the noise. The trend plus seasonality will do it.