Douglas J. Dalrymple and Barry E. King, (1981), “Selecting parameters for short-term forecasting techniques,” Decision Sciences, 12, 661-669.
Parameters for extrapolation models are often selected to reduce the error for a one-period ahead forecast horizon.
Often, however, the forecasts are made for horizons beyond one period. This study asks whether it would be worthwhile to select parameters for the specific forecast horizon. Good question. It was examined by using data for 25 business time series (“mostly monthly” they say). Using cumulative MAPEs for forecast horizons from 1 to 12 periods ahead, this search for optimum parameters led to no gain when using either exponential smoothing nor for trend regression. Dalrymple and King found some benefit for this procedure when using moving averages, but I did not draw the same conclusion form their data. This is apparently the first study on this issue. Based on these initial finding, the answer seems to be that one-period ahead searches are adequate. The paper also presents data showing the increase in error as the forecast horizon increases, and the value of including more historical data. While it did help to use more historical data fro the parameter search, their conclusion was overstated by a misprint (on p. 668) where they say 8 periods of data were optimal for trend regression for a
one-period-ahead forecast vs. 27 for a 12 period-ahead forecast. (It should have been 18 periods, not 8, for the one-period horizon.)