Using weather forecasts as exogenous data for timeseries forecasting I'm using Facebook Prophet as a forecasting model and I want to use weather data (temp for example) as additional regressor (exogenous data or external variable).
Additional regressors are integrated in a linear way into Prophet and need future values at forecast time.
My question is: If I know that I can have pretty good weather forecasts say at day-4:

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*Should I train the model using D-4 weather forecasts in the past and use the D-4 weather forecasts at prediction time ?

*Or, train the model using day's actual temperature (D-0) and then use the D-4 temperature forecast at prediction time (as if it was the same as D-0 or actual weather in 4 days) ?

EDIT
I assume in this case that the predictand has a relationship only with the actual temperature values and not with the lagged weather forecasts.

It's a good question.
I would try both and see what happens. It also kinda depends on the thing you are forecasting, for example trips to disney world may depend more on the lagged weather forecast as that requires more planning than say grocery store sales.
I understand that you are trying to incorporate the inherit bias in weather forecasting, which makes sense, but by changing the variable here you could be fundamentally answering a different question with it.
