Forecasting Sparse Demand Data: Cumulative sum transformation

Question

I have many SKUs/products that have missing historical values.

By missing, it means it has no data or order at all. I'm tempted to say intermittent but there are not regularly intermittent to make use of method like Croston model.

Also it's not helpful that we don't have an active indicator to indicate whether this product is still alive or not.

I'm thinking of transforming this very sparse demand data into a cumulative sum. For example, for the following sparse demand data

raw <- c(13,45,0,0,0,0,0,0,14,20,0,0,0,13,0,0,0)
cumsum <- c(13,58,58,58,58,58,58,72,92,92,92,92,105,105,105,105)

And then apply forecasting methods on the transformed cumulative sum instead.

We do have other methods applied like top-bottom approach, clustering with other similar SKUs, etc. But for this exercise, I want to explore this transformation approach.

Is there any literature that speaks about this transformation for forecasting? What are the models being developed specifically for this transformed data if any?

Answer 1

"Missing values" is something different than "no orders". In the first case, we don't know whether there were orders or not, in the second case we know there were none. This makes a difference.

Your raw data are what is known as "lumpy" (many zeros, high non-zero values). This is even harder to forecast usefully than non-lumpy demands (many zeros, low non-zero values).

I am not aware of anybody working on cumulative demands. One problem I see is the following. When working with cumulative demands, the natural thing to model and forecast is its growth, or the slope. Assuming you enforce an intercept of zero (which makes sense: at the beginning of your history, there should not be any historical demand, or if there is, you should just extend the history), modeling and forecasting a slope on the cumulative sums is precisely the same as modeling and forecasting an overall level on the original demands. The same holds for "local" slopes (corresponding to "local" levels) and dampening trends (corresponding to levels that decay to zero, e.g., through obsolescence).

The closest to what you are doing seems to be work on temporal aggregation. Nikos Kourentzes and Fotios Petropoulos have published a couple of articles in forecasting, production and inventory control journals on this kind of approach.