A Critical Analytical Review of Hybrid Grey Models and Their Applications in Forecasting Non-Stationary Time Series
DOI:
https://doi.org/10.29304/jqcsm.2026.18.12337Keywords:
Grey system theory; Hybrid grey models; Non-stationary time series; Forecasting; Fuzzy logic; Deep learningAbstract
Even so, forecasting non-stationary time series remains challenging due to the unavailability of data, uncertainties, and highly time-variable patterns. Due to the unique advantages of grey system theory, such as the low-data requirement, hybrid grey models have gained more and more extensive attention as hybrid models, which are realized by merging grey system theory with other intelligent methods, including fuzzy logic, artificial neural networks, met heuristic optimization, and deep learning, and have displayed significant flexibility and accuracy. This study provides a systematic and critical review of hybrid grey models, encompassing their structural framework, integration strategies, and applications in various forecasting domains. The nested, parallel, and serial hybridization approaches are then categorized, and the trade-offs between model sophistication and predictive performance are discussed. The significant drawbacks, including interpretability issues, the risks of over fitting, and the lack of standard benchmarking protocols, are also highlighted. Ultimately, the paper outlines potential research paths, including explainable AI, probabilistic reasoning, and automated mechanisms for model selection. The provided insights serve as a valuable reference for researchers and practitioners seeking to design hybrid grey forecasting models that are effective in uncertain environments.
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References
B. Li et al., “Hybrid grey–neural network models for wind energy prediction,” Renewable Energy, vol. 175, pp. 237–247, 2021.
B. Lim and S. Zohren, “Time Series Forecasting With Deep Learning: A Survey,” arXiv preprint, Apr. 2020.
B. Yousefi and M. A. Haji, “Fuzzy grey systems: An integration model for supplier evaluation under uncertainty,” Expert Systems with Applications, vol. 146, Article 113147, 2020.
C. Hsu and S. Chen, “Comparison of grey and ARIMA models in forecasting small-scale time series,” Applied Mathematical Modelling, vol. 57, pp. 415–429, 2018.
H. Han et al., “Time series forecasting model for non-stationary series pattern extraction using deep learning and GARCH modeling,” Journal of Cloud Computing, vol. 13, Article 2, 2024. [6] H. Wang, Y. Zhao, and L. Liu, “On the trade-offs between accuracy and complexity in hybrid grey forecasting systems,” Expert Syst. Appl., vol. 168, Article 114305, 2021. [7] H. Zhang, Y. Hao, and J. Li, “Hybrid grey-LSTM model for time series forecasting under data scarcity,” Expert Systems with Applications, vol. 200, Article 117002, 2022.
J. Deng, “Control problems of grey systems,” Systems & Control Letters, vol. 1, no. 5, pp. 288–294, 1982.
M. Eissa and A. B. Zeineldin, “Grey-based decision models for renewable energy integration,” Renewable Energy, vol. 180, pp. 134–145, 2021.
M. El-Gayar and A. M. Elsayed, “A nonlinear grey model for improving forecasting under irregular patterns,” Expert Systems with Applications, vol. 148, Article 113246, 2020.
M. J. Wu and H. S. Chang, “A GM(1,N) Model for Forecasting Water Demand Based on Grey Relational Analysis,” Journal of Hydrology, vol. 540, pp. 530–543, 2016.
R. A. Aliev et al., “Fuzzy grey relational analysis-based decision model for dynamic environments,” Soft Computing, vol. 25, no. 18, pp. 11923–11937, 2021.
S. Deng, H. Li, and B. Zhang, “A discrete grey prediction model for irregular data intervals,” Grey Systems: Theory and Application, vol. 11, no. 3, pp. 385–400, 2021.
S. Liu and Y. Lin, Grey Systems: Theory and Applications, Springer, 2010.
X. Ma, Y. Hao, and H. Zhang, “Grey relational analysis for incomplete systems,” Information Sciences, vol. 620, pp. 45–62, 2023.
X. Zhang and H. Sun, “Nonlinear grey forecasting model with polynomial modification,” Applied Mathematical Modelling, vol. 63, pp. 486–498, 2018.
Y. Hao and X. Ma, “A Hybrid Grey System Model Based on Stacked LSTM Layers and Its Application in Energy Consumption Forecasting,” Processes, vol. 12, no. 8, Article 1749, 2024.
Y. Li and Y. Shi, “A fuzzy grey model for uncertainty-based prediction in expert systems,” Information Sciences, vol. 426, pp. 112–125, 2018.
Y. Liu and M. Wu, “A hybrid grey model optimized by WOA for economic forecasting,” Applied Soft Computing, vol. 95, Article 106536, 2020.
Y. Wang et al., “Parameter optimization of grey prediction model using PSO and its application in electricity demand,” Energy, vol. 214, Article 118834, 2021.
Z. Cui et al., “A hybrid rolling grey framework for short time series modeling,” Neural Computing and Applications, vol. 33, pp. 11339–11353, 2021. [22] Z. Chen and H. Zhang, “Hybrid grey–ANN model for PM2.5 forecasting,” Atmospheric Environment, vol. 244, 2021.
A. A. Khan and R. Kumar, “GA-tuned GM(1,1) model for agricultural yield forecasting,” Information Processing in Agriculture, vol. 9, no. 3, pp. 412–421, 2022.
A. Author et al., “New grey forecasting model with its application and computer code,” AIMS Mathematics, vol. 6, no. 2, pp. …, 2021.
A. Kumar and R. Singh, “Fuzzy–Grey river flow prediction model,” Journal of Hydrology, vol. 595, 2021.
A. Liu and L. Yu, “Hybrid grey–ANN model for air pollution forecasting,” Environmental Modelling & Software, vol. 134, Article 104874, 2020.
A. N. Qader and K. Al-Rahimi, “Grey–ARIMA hybrid model for industrial demand forecasting,” Journal of Industrial Engineering International, vol. 17, pp. 389–400, 2021.
B. Han et al., “Forecasting with hybrid grey models using cross-validation: A robust approach,” Applied Soft Computing, vol. 118, Article 108460, 2022.
D. Huang and T. Lin, “Interval grey models with probabilistic reasoning for risk-aware forecasting,” Decision Support Systems, vol. 158, 2022.
F. Zhou et al., “Forecasting stock prices with GM–LSTM hybrid model,” Expert Systems with Applications, vol. 185, Article 115634, 2021.
H. Chen et al., “Hybrid grey forecasting model based on genetic algorithm for air pollution prediction,” Environmental Science and Pollution Research, vol. 28, no. 5, pp. 5689–5702, 2021.
H. Ma and J. Zhu, “Parameter optimization of grey forecasting model based on genetic algorithm,” Expert Systems with Applications, vol. 143, Article 113050, 2020.
H. Sun and B. Wang, “Cross-validation strategies for stochastic grey forecasting,” Mathematics and Computers in Simulation, vol. 187, 2021.
J. Armstrong, Principles of Forecasting: A Handbook for Researchers and Practitioners, Springer, 2001.
J. Tang et al., “Parameter sensitivity in grey–PSO models,” Soft Computing, vol. 24, no. 6, 2020.
K. Cheng et al., “Grey–ANN model performance under limited data scenarios,” Applied Soft Computing, vol. 101, 2021.
K. Qiu and R. Liu, “Physics-informed hybrid grey models for environmental risk forecasting,” Environmental Modelling & Software, vol. 157, 2023.
L. Deng and Z. Yao, “Fuzzy grey prediction model and its application in customer satisfaction analysis,” Expert Systems with Applications, vol. 145, Article 113112, 2020.
L. He and J. Yu, “AutoML strategies for hybrid time series forecasting,” Neurocomputing, vol. 501, 2022.
L. Wang et al., “Crop yield forecasting using GM–GA hybrid approach,” Agricultural Systems, vol. 178, 2020.
L. Zhang and Y. Wu, “Design frameworks for hybrid grey models: Challenges and prospects,” Journal of Computational Science, vol. 58, 2022.
M. Alkan and S. Yildiz, “A hybrid grey–ANN model for short-term traffic flow prediction,” Transportation Research Part C, vol. 103, pp. 61–74, 2019.
M. Ali and M. Al-Khazraji, “Grey–ARIMA hybrid models for inflation analysis,” Applied Economics, vol. 52, no. 30, 2020.
M. Cheng et al., “Benchmarking hybrid grey models: A proposal for open evaluation platforms,” Journal of Big Data, vol. 9, 2022.
M. Xiong and L. Huang, “Interpretability analysis of hybrid grey models,” Expert Systems with Applications, vol. 174, 2021.
R. Kumar and A. Kumar, “Hybrid fuzzy–grey river forecasting,” Journal of Hydrology, vol. 595, 2021.
S. A. M. Al-Fattah and M. E. Abd El Aziz, “Hybrid grey–ARIMA models for long-term load forecasting,” Alexandria Engineering Journal, vol. 60, no. 3, pp. 3197–3207, 2021.
S. Liu, Y. Lin, and N. Dang, Grey Systems: Theory and Applications, Springer, 2017.
T. A. Zawbaa et al., “Metaheuristic-based hybrid grey prediction models: A comparative study,” Soft Computing, vol. 27, pp. 14523–14539, 2023.
T. Nguyen and P. Ha, “Benchmarking hybrid grey models: A systematic review,” Sustainable Computing, vol. 30, 2023.
T. Zhang et al., “Bayesian grey models for uncertainty quantification,” Applied Mathematical Modelling, vol. 97, 2022.
X. Wang et al., “Long-term PM2.5 prediction based on grey–LSTM hybrid model with wavelet decomposition,” Atmospheric Pollution Research, vol. 13, no. 2, Article 101298, 2022.
X. Zhao et al., “Electricity price prediction using Grey–LSTM hybrid model,” Energy, vol. 239, Article 122140, 2022.
X. Zhao, L. Wang, and K. Zhang, “Grey–LSTM hybrid model for electricity price forecasting,” Energy, vol. 239, Article 122140, 2022.
Y. Feng et al., “Short-term electric load forecasting using hybrid grey–neural networks,” Energy Reports, vol. 7, pp. 5851–5860, 2021.
Y. Liu et al., “Load forecasting using GM–PSO hybrid model,” Energy Reports, vol. 6, pp. 412–420, 2020.
Y. Liu, H. Chen, and F. Yang, “Hybrid grey–PSO model for load forecasting,” Energy Reports, vol. 6, pp. 412–420, 2020.
Y. Sun and Y. Xu, “Integration of grey theory and fuzzy inference for subjective time series prediction,” Applied Soft Computing, vol. 101, Article 107017, 2021.
Y. Wang and H. Zhou, “Interpretable hybrid grey–AI forecasting with attention mechanisms,” Expert Systems with Applications, vol. 213, 2023.
Z. Chen, H. Zhang, and J. Li, “Grey–LSTM hybrid forecasting model for energy consumption prediction,” Energy AI, vol. 7, Article 100123, 2022.
Z. Li et al., “A hybrid grey–LSTM model for wind speed forecasting,” Energy Conversion and Management, vol. 254, 2022.
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Copyright (c) 2026 Ali Abdul Karim Kazem Naji
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