It seems to me that it is possible that a forecasting model does very well on one step ahead forecasts (or on any other point forecast) but performs poorly on multistep forecasts (if you average the error for all forecasts on the horizon). For example, a simple exponential smoothing model might do well on the next step ahead forecast because of the local behavior of the time series, but will perform very poorly on a multistep forecast horizon because it produces a flat forecast that ignores any trend or seasonality.

Conversely is seems possible that a model can have better generalizing properties and perform better on average on a multistep forecast horizon, but at the cost of increased error on the first step or the first few steps.

Yet all the forecasting algorithms I've seen use one step ahead point forecasts to estimate goodness of fit.

Am I missing something? Does better one step ahead accuracy always imply better multi-step accuracy?

Or is using one step ahead forecasts for goodness of fit simply a pragmatic solution because trying to optimize for multistep ahead forecasts is not feasible or practical?


2 Answers 2


For real world problems, I've found fitting a unique equation and/or coefficients for each forecast step ahead (direct forecasting) produces the most accurate prediction. It tends to limit the propagation of errors. Rob Hyndman discusses combining recursive and direct forecasting in the following link:

Combining Recursive and Direct Forecasting


This is a great question, and I think it is telling it does not have any answers (even though that might be down to the title that is bit misleading I think).

I always found it puzzling that the discussion is dominated by discussion of one-step ahead forecast, and how automatic selection algorithms for the most part ignore that there can be big difference between one-step ahead and multistep performance. In practice, there can be huge difference in performance between those, so I think you are right that this is mostly down to convenience. That said, I often find it that people are not aware of this, so it might be also ignorance.


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