How do I set up a time series model to predict percentages across time that need to aggregate up to 100%?

1

Hello.

I have come to a happy place with my monthly sales forecasting model. However, we now need to be able to forecast at the day level for the two months from the current date in order to make time sensitive decisions.

We cannot “just” make another forecasting model at the day level aggregate because when “month 3” becomes “month 2”, the forecast either has big jumps or dips (due to moving from one model to the next.) To combat this, a consultant stated to use the day model to get percentages of sales across each day of the month and apply those to our near term monthly model to disaggregate.

I would like to experiment with changing our target variable from actual sales units, to the percentage of sales for “x” day itself. However, I’m not sure how, or if, I can ensure the sum of each day’s posterior sales percentage would sum up to 1. Or do I even need to?

Either way, I’m not sure how I would set this model up. If I have 8 predictors and essentially, 28 to 31 targets (depending on how many days are in the month), what type of model should I use and how should that model theoretically be structured?

2

I’m not sure I totally understand, but it sounds like you want to do forecast reconciliation between your daily and monthly models?

3

Yes. At its simplest form, I want to predict the percentage of the months sales for each day within the month.

4

You could use a mutlinomial likelihood if you want the percentages to be latent, or you could use a dirichlet likelihood if you want to predict the percentages directly.

What do you mean by this? If you have a daily model, it doesn’t know anything about moving from one month to the next.

5

Ahh! Helpful as always! Thank you Jesse.