  Multi-step ahead forecasting is still an open challenge in time series
forecasting. Several approaches that deal with this complex problem have been
proposed in the literature but an extensive comparison on a large number of
tasks is still missing. This paper aims to fill this gap by reviewing existing
strategies for multi-step ahead forecasting and comparing them in theoretical
and practical terms. To attain such an objective, we performed a large scale
comparison of these different strategies using a large experimental benchmark
(namely the 111 series from the NN5 forecasting competition). In addition, we
considered the effects of deseasonalization, input variable selection, and
forecast combination on these strategies and on multi-step ahead forecasting at
large. The following three findings appear to be consistently supported by the
experimental results: Multiple-Output strategies are the best performing
approaches, deseasonalization leads to uniformly improved forecast accuracy,
and input selection is more effective when performed in conjunction with
deseasonalization.
