Multiple-output modeling for multi-step-ahead time series forecasting

Souhaib Ben Taieb, Antti Sorjamaa and Gianluca Bontempi
(2010) Neurocomputing, 73(10-12):1950–1957, 2010.


Accurate prediction of time series over long future horizons is the new frontier of forecasting. Conventional approaches to long-term time series forecasting rely either on iterated one-step-ahead predictors or direct predictors.

In spite of their diversity, iterated and direct techniques for multi-step-ahead forecasting share a common feature, i.e. they model from data a multiple-input single-output mapping. In previous works, the authors presented an original multiple-output approach to multi-step-ahead prediction. The goal is to improve accuracy by preserving in the forecasted sequence the stochastic properties of the training series. This is not guaranteed for instance in direct approaches where predictions for different horizons are performed independently.

This paper presents a review of single-output vs. multiple-output approaches for prediction and goes a step forward with respect to the previous authors contributions by (i) extending the multiple-output approach with a query-based criterion and (ii) presenting an assessment of single-output and multiple-output methods on the NN3 competition datasets.

In particular, the experimental section shows that multiple-output approaches represent a competitive choice for tackling long-term forecasting tasks.