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My demand forecasting solution generates point forecasts and forecast intervals for millions of time series (# of products × # stores for a large retailer) using statistical models.

Business users (i.e. with no stats knowledge) can go in an adjust some of those forecasts based on their experience and business plans. When they do so, they only adjust the point forecast (typically for a few thousand forecasts out of the 2~3 million that are generated each week).

How can the forecast intervals be calculated for the user adjusted forecasts?

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You could simply adjust the limits by the difference between the two values. More generally one could include a predictor variable reflecting the user's specified probability of a particular event happening next period.

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  • $\begingroup$ Thanks. "You could simply adjust the limits by the difference between the two values." - that was my first thought, but then consider the following scenario: I have a point forecast of 4 units, with a +/- 1 forecast interval, so my forecast is expected to be within [3,5] with a certain probability. The user then adjusts it up to 25 units, now my forecast is expected to fall within [24,26], which conveys a much higher level of confidence than my original forecast interval. How would you deal with that? $\endgroup$ – Skander H. Mar 11 '19 at 18:36
  • $\begingroup$ If (and I don't know why ) you think that uncertainty should change with level then take the original standard deviation and multiply it by the addend to compute a modified standard deviation and use it estimate the new limits around the new expected value. Your modelling software should be checking on the assumption of a constant error variance over time and if it is I don't think you have a worry. $\endgroup$ – IrishStat Mar 11 '19 at 19:10

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