I have implemented a leave one out cross validation to calculate errors between daily forecast and observed values for spatio-temporal data taken in a given season (summer say). I have further implemented a vector stationary block bootstrap (SBB) to account for the spatial and temporal correlation to calculate RMSE and the corresponding confidence intervals (CIs). I am also comparing multiple forecast methods (m) so I repeat the above procedure for each method.
To further complicate things, I have data for the same time period (season) for n years so I actually have n RMSE and CI values for each forecast method.
What is the best approach to get an overall RMSE (over all years) for each method?
(Note, the time periods from one year to the next are not contiguous so the bootstrap can only be applied within each year)