In this paper, we report experimental results from augmenting Recurrent Neural Networks (RNN) with multi-step-ahead strategies for traffic speed prediction. For multi-step-ahead time series forecasting, researchers have applied MIMO, recursive, and direct strategies to machine learning methods in other domains. We applied the recursive and direct strategies to the GRU networks for predicting multi-step-ahead traffic speed and compared the prediction errors with the GRU network without the strategies (i.e. Based on the results from the experiments, we found that the direct strategy and the MIMO strategy produce models with smaller error metrics as compared to the recursive strategy. The direct strategy is computationally very expensive, thus MIMO strategy i.e. the GRU architecture without any strategy, is our preferred recommendation.

An accurate prediction of crude oil prices over long future horizons is challenging and of great interest to governments, enterprises, and investors. This paper proposes a revised hybrid model built upon empirical mode decomposition (EMD) based on the feed-forward neural network (FNN) modeling framework incorporating the slope-based method (SBM), which is capable of capturing the complex dynamic of crude oil prices. Three commonly used multi-step-ahead prediction strategies proposed in the literature, including iterated strategy, direct strategy, and MIMO (multiple-input multiple-output) strategy, are examined and compared, and practical considerations for the selection of a prediction strategy for multi-step-ahead forecasting relating to crude oil prices are identified. The weekly data from the WTI (West Texas Intermediate) crude oil spot price are used to compare the performance of the alternative models under the EMD-SBM-FNN modeling framework with selected counterparts. The quantitative and comprehensive assessments are performed on the basis of prediction accuracy and computational cost. The results obtained in this study indicate that the proposed EMD-SBM-FNN model using the MIMO strategy is the best in terms of prediction accuracy with accredited computational load.

Multi-step-ahead time series prediction is one of the most challenging research topics in the field of time series modeling and prediction, and is continually under research. Recently, the multiple-input several multiple-outputs (MISMO) modeling strategy has been proposed as a promising alternative for multi-step-ahead time series prediction, exhibiting advantages compared with the two currently dominating strategies, the iterated and the direct strategies. Built on the established MISMO strategy, this study proposes a particle swarm optimization (PSO)-based MISMO modeling strategy, which is capable of determining the number of sub-models in a self-adaptive mode, with varying prediction horizons. Rather than deriving crisp divides with equal-size s prediction horizons from the established MISMO, the proposed PSO-MISMO strategy, implemented with neural networks, employs a heuristic to create flexible divides with varying sizes of prediction horizons and to generate corresponding sub-models, providing considerable flexibility in model construction, which has been validated with simulated and real datasets.