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.
Best Answer
One approach here is simply to test your data-- holdout the last N periods from your data, fit an exponential smoothing model, and look at the MAPE or other error metrics for the lags you're interested in. Then vary the parameters slightly and see what happens to the error for the different lags. You may need to do this for some other values of N as well to get a decent data set.