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Beyond One-Step-Ahead Forecasting: Evaluation of Alternative Multi-Step-Ahead Forecasting Models for Crude Oil Prices
Tao Xiong, Yukun Bao, Zhongyi Hu
TL;DR
Long-horizon crude oil price forecasting requires evaluating both prediction accuracy and computational cost across alternative multi-step strategies. This paper proposes an EMD-SBM-FNN framework and compares iterated, direct, and MIMO strategies using WTI weekly data. EMD-SBM-FNN with MIMO delivers high-quality forecasts with accredited computational load, while the study is limited to point forecasting without uncertainty information.
Problem
Prior studies focused exclusively on prediction accuracy, leaving computational modeling cost insufficiently considered despite its relevance to investment decision-making.
Method
The paper proposes EMD-SBM-FNN and empirically compares iterated, direct, and MIMO strategies for multi-step-ahead WTI crude oil price forecasting.
Results
EMD-SBM-FNN using MIMO provides high-quality multi-step-ahead crude oil price forecasts with accredited computational loads.
Takeaways & Limitations
MIMO is recommended as a promising prediction technique for multi-step-ahead crude oil price forecasting.
Takeaways & Limitations
The study restricts attention to point forecasting and therefore provides no information about forecast uncertainty.
Abstract
from arXiv · showhide
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.
Research Highlights
The study proposes EMD-SBM-FNN for multi-step-ahead crude oil price forecasting and compares iterated, direct, and MIMO strategies. EMD-SBM-FNN with MIMO is reported as best for prediction accuracy, while iterated uses the lowest computational load.
- EMD-SBM-FNN is proposed for multi-step-ahead crude oil price forecasting.
- The study provides empirical evidence comparing iterated, direct, and MIMO multi-step-ahead prediction strategies.
- EMD-SBM-FNN using MIMO is reported as best for prediction accuracy with accredited computational load.
- Direct and MIMO strategies achieve the best prediction performance.
- Iterated strategy achieves the lowest computational load.
1. Introduction
The study addresses the limited evaluation of long-horizon crude oil price forecasting by developing a revised EMD-based FNN framework and comparing three multi-step-ahead prediction strategies. It focuses on improving forecasting performance while examining which strategy should be preferred in practice.
- Research gap: Prior crude oil forecasting research has focused mainly on one-step-ahead prediction, providing limited evidence about long-horizon performance.The introduction identifies limited use in comparing one-step-ahead forecasts when the goal is understanding long-term future behavior.
- Motivation: Multi-step-ahead forecasting is more informative for assessing long-term crude oil price behavior than one-step-ahead forecasting, but it faces accumulating errors, uncertainty, and missing future information.Crude oil prices are described as highly nonlinear and difficult to forecast, especially over multiple future steps.
- Research objectives: The study comparatively examines iterated, direct, and MIMO strategies for multi-step-ahead crude oil price forecasting.The paper identifies prediction strategy as one of two fundamental modeling issues and evaluates the three leading strategies in the crude oil context.
- Method: The proposed EMD-SBM-FNN framework extends EMD-FNN by incorporating a slope-based method to restrain the EMD end effect.The end effect is described as negatively affecting modeling quality and overall prediction performance.
- Contributions: The paper aims to determine whether EMD-based FNN superiority holds consistently for multi-step-ahead forecasting and which prediction strategy should be preferred in practice.These questions are framed as unresolved empirical issues in the crude oil forecasting literature.
2. Literature review
Prior research on multi-step-ahead energy forecasting spans hybrid neural, wavelet, decomposition, statistical, and machine-learning models, but crude-oil evidence and strategy comparisons remain limited. This study compares iterated, direct, and MIMO strategies while also considering computational cost and weekly WTI data.
- Only six of the reviewed 19 studies concern crude oil prices, leaving a limited research base.
- Most reviewed studies use iterated or direct strategies, while seven do not clearly report their prediction strategy.
- No reviewed study compared iterated and direct strategies for multi-step-ahead crude-oil forecasting alongside MIMO.
- Previous studies generally used hourly, daily, or monthly data rather than weekly data, which this study adopts for multi-step forecasting.
- Earlier work focused exclusively on prediction accuracy, whereas this study evaluates both accuracy and computational cost.
- The study addresses reported weaknesses of EMD-NNs by targeting end effects that distort decomposed sub-series and affect subsequent modeling.
3. Methodologies
The paper compares iterated, direct, and MIMO multi-step forecasting strategies within a revised EMD-SBM-FNN framework. The framework decomposes crude-oil prices, models components separately, and aggregates their forecasts for the original series.
- Prediction strategies: The iterated strategy fits one one-step-ahead model and recursively feeds predictions back as inputs until the chosen horizon.
- Prediction strategies: Iterated forecasting requires only one model but accumulates errors across successive predictions, potentially degrading accuracy at longer horizons.
- Prediction strategies: The direct strategy estimates a separate model for each horizon using only past observations, avoiding input feedback from previous predictions.
- Prediction strategies: MIMO predicts a vector of future values with one multiple-output model, preserving temporal stochastic dependency among predicted values.
- EMD-SBM-FNN: The proposed EMD-SBM-FNN applies SBM during EMD sifting to restrain end effects, models each extracted component with an FNN, and aggregates component forecasts.
4. Research design
The research design uses weekly WTI crude-oil prices, multiple forecasting horizons, a holdout evaluation, and three accuracy criteria. Models are selected and tested separately for iterated, direct, and MIMO strategies, with computational cost also assessed.
- Data and evaluation: The first 418 observations form the estimation sample and the final 208 observations form the holdout sample.
- Data and evaluation: Models are trained on the estimation sample, forecast across the holdout sample, and are evaluated by comparison with the heldout observations.
- Performance measures: Performance is assessed using SMAPE and MASE for level prediction and directional symmetry for direction prediction.
- Statistical testing: The SPA test evaluates whether competing models statistically outperform a base model under prespecified loss functions.
- Model selection: For each horizon, input and model selection use filtering and fivefold cross-validation before testing the selected models on holdout samples.
5. Results
The revised EMD-based models generally outperform FNN, with EMD-SBM-FNN leading across accuracy comparisons. Direct and MIMO strategies are more accurate than iterated forecasting, while MIMO offers strong accuracy without a large computational burden.
- The top three SMAPE models are EMD-SBM-FNN with direct strategy, EMD-SBM-FNN with MIMO strategy, and EMD-FNN with MIMO strategy.
- The top three MASE models are EMD-SBM-FNN with MIMO strategy, EMD-SBM-FNN with direct strategy, and EMD-FNN with MIMO strategy.
- EMD-SBM-FNN and EMD-FNN consistently forecast more accurately than FNN across the three prediction strategies.For H = 20 or 24, both EMD-based models improve SMAPE by over 15%.
- EMD-SBM-FNN generally outperforms EMD-FNN, supporting the value of addressing the end effect in original EMD.
- Direct and MIMO strategies consistently achieve more accurate forecasts than the iterated strategy across horizons and modeling techniques.The paper suggests that accumulated errors in iterated forecasting deteriorate accuracy.
- MIMO and direct strategies perform similarly overall, with eight of eighteen best models using direct forecasting and the remainder using MIMO.For medium- and long-term horizons, MIMO is only marginally better than direct forecasting.
- The iterated strategy is least expensive, but its computational-cost advantage over MIMO is negligible; both are four times faster than DIR-SVR.The direct strategy has obviously higher computational cost than iterated and MIMO strategies.
6. Conclusions
The study evaluates revised EMD-based FNN models and three multi-step forecasting strategies for crude oil prices. EMD-SBM-FNN with MIMO provides high-quality forecasts with accredited computational loads, while the study identifies scope boundaries involving alternative decompositions and point-only forecasts.
- The study evaluates revised EMD-based FNN models and compares three leading multi-step-ahead prediction strategies for crude oil prices.
- EMD-SBM-FNN using MIMO is a promising technique with high-quality forecasts and accredited computational loads.
- The proposed framework may also apply to difficult multi-step forecasting tasks such as energy consumption, but this requires further study.
- Further research is recommended on EEMD, described as a substantial improvement over original EMD.
- The study restricts attention to point forecasts, which provide no information about forecast uncertainty.The authors identify interval forecasts as more valuable to energy-market decision-makers and reserve them for future research.
Figures
The figures present the EMD with slope-based method, the proposed EMD-SBM-FNN framework, and the experimental procedure for multi-step-ahead crude oil-price forecasting.
- Figure 1 presents the EMD with slope-based method.
- Figure 2 presents the proposed EMD-SBM-FNN modeling framework for multi-step-ahead forecasting.
- Figure 3 presents the experiment procedures for multi-step-ahead forecasting of crude oil price.
Tables
The tables organize prior multi-step-ahead forecasting studies, prediction-accuracy measures, SPA tests, and elapsed computational times across prediction horizons.
- Table 1 surveys studies using different modeling techniques, time scales, prediction horizons, and forecasting strategies.
- The proposed modeling framework uses EMD-SBM-FNN with iterated, direct, and MIMO strategies for crude oil-price forecasting.
- Table 2 reports prediction-accuracy measures for the hold-out sample, with the smallest value generally identified as best.
- Table 3 reports SPA tests for various prediction models across prediction horizons under a prespecified loss function.
- Table 4 reports the elapsed time required by examined models for each prediction horizon.