I asked a variation of this question, but I want to be more direct.
Take the exact same Triple Exponential Smoothing Model (Holt-Winters with a moving level, trend, and seasonal component)---
Would or would not --- the smoothing parameters alpha, beta, and gamma (determining the weight of recent data on level, trend, and seasonality, respectively) ----
be optimized differently for different forecast horizons? ... aka t+1 periods vs. t+2 periods, t+6 periods, t+12 periods, etc.?
My initial hunch ... is yes.
The nature of Holt-Winters is that to forecast 6 periods out (weeks, months, whatever) -- you take the current level, add 6 times the calculated trend, and multiply (or add) by the seasonality of the last corresponding period.
It just seems like common sense that a 'recent data' chasing model would, in many cases, be more accurate for a horizon of t+1, and a poorer for a long term, t+6 model. BUT, I definitely can be wrong on that.
I just don't see this discussed anywhere, and perhaps I have some gaps in knowledge on this parameter optimization process, and perhaps I'm overfitting models.
When specialized software typically optimizes these values --- I assume against test data or what-have-you, minimizing MSE or MAPE ... does this software minimize the MAPE against t+1 forecasts, or t+6 forecasts, or both, or every horizon? This is what confuses me.
