# Time series forecasting when there is a capacity limit. Or in other words bounded forecasting

Ideas for dealing with bounding time series forecasting?

My time series which are sales were limited for certain days in the past. For example, there was a capacity constraint on a day e.g. 1000 orders hence the orders reached this limit while they could had exceed it e.g. 1200 orders.

However, the tricky part of those capacity limits is that they were not constant over time. For example, the business saw that they were reaching full capacity so they took measures to increase it for a bit for future days until maximum capacity was reached again.

Now, I want to forecast the same time series but the capacity limit does not exist anymore.

Furthermore, I give a representative simple example:

y_variable___ = [ 5, 9, 6, 9, 9, 15, 9 , 14, 15, 25, 20, 18, 26]

max_capacity = [ 9, 9, 9, 9, 9, 15, 15, 15, 15, 25, 25, 25, 29]

So in the cases that the sales are reaching maximum capacity I probably have some unforeseen sales, or in other words I could had more sales.

Any ideas on how to deal with that?

Thanks!

• One easily implemented approach would be to flag the bounded days with a 0,1 dummy predictor. Then run the adjusted forecast model including that predictor.
– user234562
Mar 14, 2020 at 12:47
• If I do that, then the model will understand that when I have at the dummy 1 (bounded day) I also have high sales and the opposite. So if set the dummy as 0 at the forecast sample then I will have lower sales which is actually the opposite to reality. If I set it to 1 then I will predict higher number of sales but probably for all the forecast days. Mar 14, 2020 at 15:05