In https://peerj.com/preprints/3190.pdf section 4.3
SHFs simulate the errors we would have made had we used this
forecasting method at those points in the past.
The meaning I could understand is change "had" to "when", like
SHFs simulate the errors we would have made when we used this forecasting method at those points in the past.
I can't understand what is this "had" used for.
Best Answer
"had we used this forecasting method" means that the forecasters did not use that forecasting method in the past, but if they had, then a certain amount of error would have occurred. SHF is a technique to simulate what those hypothetical errors would have been.
In short we are dealing with an unreal past here, which is why the "had"-form is used.
I really think this paper may not be the best example to work on.