I have several time series forecasts for a variable I'm working with, where I'm producing forecasts for a number of individual countries. In order to do the forecasting I am using the recently open-sourced Prophet algorithm from Facebook.
There is value in forecasting at the level of individual countries, because then each time-series model ends up with a country specific trend and seasonality components, as well as the model allowing for holidays to be included, which are of course also country dependent.
What I'd like to do is basically roll these forecasts up into a continental or worldwide forecast, but I'm not sure about the most rigorous way to treat the uncertainties. The naive approach is of course just to sum the maximum and minimum values of the uncertainty from each forecast to find the worldwide level uncertainty, but this doesn't seem like the correct approach.
Has anyone got any suggestions for a sensible approach to this (even if it requires certain assumptions about the data or the model)?
One suggestion in the comments was to look at the shape of the distributions in order to answer this question. The top plot that I show here are the raw distributions (for a single year) for the variable of interest, and the log-distributions are in the plot below.