Can you combine Facebook Prophet (fbprophet) with ARMA? I am new to dealing with time-series data, so my apologies if this is not a valid question.
I am wondering if there is a way to combine ARMA with fbprophet. From what I understand, fbprophet can take into account holidays and other seasonalities, but ARMA can take advantage of output variables ("y") and residuals from the past to predict.
Does it make sense to add "y" from the past as features in fbprophet and treat them as extra regressors? Would that be essentially the same thing as combining fbprophet with AR? How would I create features for the MA part if I wanted to combine that with fbprophet too?
 A: Prophet is a GAM so of course you could do something where you model your ar process on your y independently then take the residuals and fit a prophet model with those residuals (the MA component) and the lagged y as the extra variables.
Now, would this be good? Probably not.
It most likely would just mess with the trend changepoint output from Prophet since it has stricter priors on those terms than on the variables you are passing it and it would probably favor your variables more to get the level of the series at any point in time. Prophet is modelling more than just for holidays and events, it is also modelling seasonality (using fourier basis functions) and a switchpoint model for the trend, and I would probably let it do its thing for the time related signals.
But, as with anything, it might add value and could be tested!  However, if your forecast horizon is long then feeding those ar terms could cause significant issues and the trend component from Prophet would probably be a more stable solution.
