I've been playing around with fbprophet here and I've noticed they specify their base additive model is
$$y(t) = g(t) + s(t) + h(t) + \epsilon_t$$
My question is two-fold:
1) How does modifying the seasonality_mode='multiplicative' affect the model? does the equation become
$$y(t) = g(t)\times s(t) + h(t) + \epsilon_t$$ or $$y(t) = g(t)\times s(t) \times h(t) + \epsilon_t$$ or something completely different?
2) If I add an additional regressor, $r$, does the equation become $$y(t) = g(t) + s(t) + h(t) + \alpha r + \epsilon_t$$ where $\alpha$ is some coefficient that is fitted to the value of $r$ or $$y(t) = g(t) + s(t) + h(t) + f(r) + \epsilon_t$$ where $f(r)$ is a function that is constructed similarly to $g(t)$?
I couldn't find much in the paper or in the documentation to explain how these modifications actually change the underlying model
