Background: My background is in statistics, but I have very little experience in working with time series data, so please go easy on me if I'm not making sense :)
Case Study: Let's suppose I would like to forecast honey output in the next quarter. I have data about historical honey outputs as well as a few other variables such as weather conditions, the number of active beehives and so on (note: these are not going to be known for the period I will be forecasting).
Problem: This seems like a classical time series problem, however, most time series methods either (1) cannot make use of extraneous regressors or (2) require these regressors to be known for the period we are trying to forecast.
Question 1: Are there time series methods out there that can indeed make effective use of extraneous data that will not be known for the period we are forecasting? If so, why are they not popular? Is it because the lagged response variable tends to give us sufficient amount of information anyway?
Question 2: Can this problem be reformulated as a general regression on lagged inputs (after removing seasonality and trend)? If so, are there any reasons I may still choose to stick to the time series approach?
Question 3: Based on the description of the case study, is there any particular method that you could recommend? (e.g. Bagged ETS, TBATS, NNs, ARIMA. etc)
Resources: Lastly, if you can recommend any particular resources or libraries (preferably in R), please do let me know.