I want this to be a general question as it may help others in the future but I will give the specifics of what I'm doing.
I am producing forecasts for many time series with different models. It is akin to using the automatic functionality of R forecast or SAS Forecast Server or ForecastPro, but the optimizing of models is based on what you could describe as our own semi-supervised ML process we've built on top of it. The forecasts are produced using SAS PROC UCM and any given forecast may utilize level, slope and seasonality in addition to some predictors.
PROC UCM does not have a damped trend option. SAS in general does not offer the full range of ESM options when it comes to damped trends-- PROC ESM, which I also use for something else, just offers one damped trend option. I want to dampen the trend in some cases and am going to do so by re-calculating the level/slope using the standard formula (you can find in Hyndman's Forecasting Principles text), comparing to the undamped slope, and adjusting the forecast for the difference.
Now to my question: after I adjust a point forecast (regardless of the reason), I believe I should also adjust the prediction interval. Let's assume (as in my case) that the prediction interval was calculated by the software when the point forecast was produced, rather than through some other method that could be done post-adjustment, and that I want to stick with that original interval as my baseline. I can think of a few options for adjustment to CI:
- do not adjust at all
- use the same nominal adjustment as what is done to the point forecast (if point forecast is adjusted down by 5, then adjust CI high and low down by 5)
- use the same percentage adjustment (adjust CI by whatever % the point forecast was adjusted)
- something more complex (your ideas appreciated)
What would you recommend and why?
