I'm still trying to expand my statistics and forecasting technique knowledge.
Right now I'm forecasting seasonal contact patterns, so the simplest model I can understand with seasonality is a Holt-Winters/ Triple exponential smoothing model.
For many of our decisions, we not only need predictions for one month out, but also two months out, and even as far as 6 months out, or more.
Obviously accuracy increasingly goes out the window as you try to forecast 6 months out, but, I guess we do what we can.
The first thing I immediately noticed after creating the triple exponential smoothing model and initiated the seasonal/ trend values — is that there are certainly different 'optimal' alpha (level), beta (trend) and gamma (seasonality) values, depending on whether you are forecasting one month out, or 6 months out.
As you might have guessed, the 1-month forecast has far greater accuracy for a test data set with a higher alpha value (stronger recent values) — and the 6 month is better with a lower alpha value.
Not that it matters much, but the 2 month is closer to the 1 month model, and the 3-4-5 seems to be closer to the 6 month, but they all have their local 'optimal' values.
So if I need a rolling forecast for the next 6 months — am I to use one model, or am I supposed to use a different set of alpha-beta-gamma values depending on how far out the predicted value is?
I have a minor background in statistics, but I know it's easy to misuse/ misread them. I don't know if using two or three different models like this can lead to mistakes.
Best Answer
What you are talking about is using a "direct" forecasting strategy rather than the more popular "recursive" forecasting strategy.
In a recursive strategy, one model is fitted, usually based on minimizing the one-step forecast mean squared error, and the forecasts for all future horizons are estimated by iterating the equations over time. If the model is linear, and the same as the data generating process, this is optimal. But in reality, the model is at best an approximation to whatever generated the data, and most real-world phenomena are non-linear.
Contrary to what @Tom Reilly asserts, there is considerable academic literature on this problem, but very little software implements alternatives to the recursive approach. The problem is addressed, and some of the associated literature is referenced, in my recent paper with Souhaib Ben Taieb: https://robjhyndman.com/publications/boostingar/
The bottom line is that you should try different approaches and choose what works best for your problem. In this case, I suggest you try the direct approach (with different parameters for different horizons) and compare the forecast accuracy with what you get using the recursive approach.