A Hybrid Stacking Ensemble Approach for Rainfall Time Series Forecasting
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Rainfall forecasting plays a crucial role in hydrology, agriculture, water resource management, and disaster mitigation. However, rainfall data typically exhibit fluctuating, seasonal, and nonlinear characteristics, which make the forecasting process quite complex. In this study, we propose a hybrid multi-model stacking ensemble to improve rainfall prediction accuracy in Kediri Regency. Our framework integrates statistical models—namely the Seasonal Autoregressive Integrated Moving Average (SARIMA) and Holt-Winters models—with machine learning and deep learning models, specifically Random Forest and Long Short-Term Memory (LSTM). We use Linear Regression as a meta-learner to combine predictions from all base models. The dataset contains monthly rainfall records from 2009 to 2022. Various preprocessing techniques are applied to the dataset, primarily normalization, lag feature construction, stationarity testing, and time-series data transformation, to enable deep learning. We use the Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) to evaluate each model's predictions. In the experiments, the ensemble stacking model outperformed the other models, with an MAE of 28.56, MSE of 1053.26, RMSE of 32.45, and MAPE of 13.05%. The results of the models used in the experiments, including the standalone SARIMA and Holt-Winters models, Random Forest, and LSTM, also showed inferior performance. Our model forecasted rainfall over the next 12 months while preserving historical seasons and data fluctuations, supporting the claim that the hybrid stacking ensemble method optimizes the accuracy, stability, and robustness of rainfall prediction for complex time-series data.
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1] Fu, K., Sun, X., Chen, K., Mo, L., Xiao, W., & Liu, S. Monthly Runoff Prediction Based on Stochastic Weighted Averaging-Improved Stacking Ensemble Model. Water (Switzerland), 16(24). https://doi.org/10.3390/w16243580. 2024.
[2] Yuan He, G. A multi-model stacked ensemble architecture with Bayesian optimization: Advancing remaining useful life estimation in aircraft engines. Measurement: Journal of the International Measurement Confederation, 263. https://doi.org/10.1016/j.measurement.2025.120199. 2026.
[3] Liu, Q., Yu, D., Xue, Y., Liu, X., & Yang, S. Multi-model ensemble with cross-domain robust stacking for heating season electricity consumption prediction. Energy and Buildings, 353. https://doi.org/10.1016/j.enbuild.2025.116908. 2026.
[4] Zhang, Y., Ji, Y., Sun, X., & Zhao, S. Sea Surface Wind Speed Retrieval from GNSS-R Using Adaptive Interval Partitioning and Multi-Model Ensemble Approach. Journal of Marine Science and Engineering, 13(12). https://doi.org/10.3390/jmse13122303. 2025.
[5] Qian, H., Bao, N., Meng, D., Zhou, B., Lei, H., & Li, H. Mapping and classification of Liao River Delta coastal wetland based on time series and multi-source GaoFen images using stacking ensemble model. Ecological Informatics, 80. https://doi.org/10.1016/j.ecoinf.2024.102488. 2024.
[6] Ganie, S. M., Dutta Pramanik, P. K., & Zhao, Z. Enhanced and Interpretable Prediction of Multiple Cancer Types Using a Stacking Ensemble Approach with SHAP Analysis. Bioengineering, 12(5). https://doi.org/10.3390/bioengineering12050472.
[7] Viedienieiev, V. A. Ensemble Forecasting Methods in DCF Modelling of the Fair Value of Enterprises. Universal Journal of Accounting and Finance, 9(4), 869–874. https://doi.org/10.13189/ujaf.2021.090432. 2021.
[8] Liang, Y. C., Maimury, Y., Chen, A. H. L., & Juarez, J. R. C. Machine learning-based prediction of air quality. Applied Sciences (Switzerland), 10(24), 1–17. https://doi.org/10.3390/app10249151. 2020.
[9] Yuan, J., Liu, Y., & Yang. Prediction of Traction Power Consumption for Rail Transit Based on Ensemble Learning Hybrid Time Series Models. In Journal of Advanced Transportation (Vol. 2025, Number 1). John Wiley and Sons Ltd. https://doi.org/10.1155/atr/8828434. 2025.
[10] Qiu, L., Cheng, C., Shi, H., Wang, X., Wang, T., & Ye, H. Stack-CBHNet: A Stacked Ensemble Learning Approach for Cloud Base Height Estimation. 2025 7th International Conference on Frontier Technologies of Information and Computer (ICFTIC), 129–133. https://doi.org/10.1109/icftic68075.2025.11324892. 2026.
[11] Mishra, P., Mahajan, A., Kumar, P., & Garg, P. Multi-Model Ensemble Learning Prediction of Surface Air Temperature in Four Major Metro Cities: A Stacking-Based Approach. 2025 Global Conference in Emerging Technology, GINOTECH 2025. https://doi.org/10.1109/GINOTECH63460.2025.11077110. 2025.
[12] Han, S. H., Mutahira, H., & Jang, H. S. Prediction of Sensor Data in a Greenhouse for Cultivation of Paprika Plants Using a Stacking Ensemble for Smart Farms. Applied Sciences (Switzerland), 13(18). https://doi.org/10.3390/app131810464. 2023.
[13] Haque, R., Khan, M. A., Rahman, H., Khan, S., Siddiqui, M. I. H., Limon, Z. H., Swapno, S. M. M. R., & Appaji, A. Explainable deep stacking ensemble model for accurate and transparent brain tumor diagnosis. Computers in Biology and Medicine, 191. https://doi.org/10.1016/j.compbiomed.2025.110166. 2025.
[14] Jiang, X., Yang, Z., Mei, H., Zheng, M., Yuan, J., & Wang, L. An Ensemble Learning Approach for Landslide Susceptibility Assessment Considering Spatial Heterogeneity Partitioning and Feature Selection. Remote Sensing, 17(16). https://doi.org/10.3390/rs17162875. 2025.
[15] Hossain, M. F., Diya, S. T., & Khan, R. ACD-ML: Advanced CKD detection using machine learning: A tri-phase ensemble and multi-layered stacking and blending approach. Computer Methods and Programs in Biomedicine Update, 7. https://doi.org/10.1016/j.cmpbup.2024.100173. 2025.
[16] Alqahtani, A. F., & Ilyas, M. An Ensemble-Based Multi-Classification Machine Learning Classifiers Approach to Detect Multiple Classes of Cyberbullying. Machine Learning and Knowledge Extraction, 6(1), 156–170. https://doi.org/10.3390/make6010009. 2024.
[17] Yoon, T., & Kang, D. Multi-Modal Stacking Ensemble for the Diagnosis of Cardiovascular Diseases. Journal of Personalized Medicine, 13(2). https://doi.org/10.3390/jpm13020373. 2023.
[18] Chen, X., Liu, J., & Wu, C. Multi-class financial distress prediction based on hybrid feature selection and improved stacking ensemble model. Expert Systems with Applications, 282. https://doi.org/10.1016/j.eswa.2025.127832. 2025.
[19] Gu, J., Liu, S., Zhou, Z., Chalov, S. R., & Zhuang, Q. A Stacking Ensemble Learning Model for Monthly Rainfall Prediction in the Taihu Basin, China. Water (Switzerland), 14(3). https://doi.org/10.3390/w14030492. 2022.
[20] Nadzirah Adnan, N., & Khalid Awang, M. (2025). A Multi-Level Stacking Ensemble Model Optimized by Soft Set Theory for Customer Churn Prediction. In IJACSA) International Journal of Advanced Computer Science and Applications (Vol. 16, Number 7). doi: 10.14569/IJACSA.2025.0160775. 2025.
[21] Makwana, S., Vaghela, D., Chan, C. K., & Naik, N. Novel hybrid approach of random forest and stacking ensemble to improve fresh water yield prediction in mobile wick solar still. Desalination and Water Treatment, 324. https://doi.org/10.1016/j.dwt.2025.101490. 2025.
[22] Liu, Y., Jiang, Z., & Leng, W. A Study on Predicting Natural Gas Prices Utilizing Ensemble Model. Sustainability (Switzerland), 17(18). https://doi.org/10.3390/su17188514. 2025.
[23] Peng, Y., Hu, Z., Hua, L., Qin, X., Zheng, J., & Hu, Q. Adaptive Stacking ensemble model driven by multi-source data fusion for energy consumption prediction in forging production line. Energy, 341. https://doi.org/10.1016/j.energy.2025.139447. 2025.
[24] Hou, H., Liu, C., Wang, Q., Zhao, B., Zhang, L., Wu, X., & Xie, C. Load Forecasting Combining Phase Space Reconstruction and Stacking Ensemble Learning. IEEE Transactions on Industry Applications, 59(2), 2296–2304. https://doi.org/10.1109/TIA.2022.3225516. 2023.
[25] Chithra Rani, P. R., & Baalaji, K. Deep learning-based ensemble stacking for enhanced intrusion detection in IoT-edge platforms. Discover Applied Sciences, 7(8). https://doi.org/10.1007/s42452-025-06871-z. 2025.
[26] Lin, S., Nong, X., Luo, J., & Wang, C. A Novel Multi-Model Stacking Ensemble Learning Method for Metro Traction Energy Prediction. IEEE Access, 10, 129231–129244. https://doi.org/10.1109/ACCESS.2022.3228441. 2022.
[27] Ali, T. E., Chong, Y. W., Manickam, S., Yusoff, M. N., Yau, K. L. A., & Zoltan, A. D. A Stacking Ensemble Model with Enhanced Feature Selection for Distributed Denial-of-Service Detection in Software-Defined Networks. Engineering, Technology and Applied Science Research, 15(1), 19232–19245. https://doi.org/10.48084/etasr.8976. 2025.
[28] Shafieian, S., & Zulkernine, M. Multi-layer stacking ensemble learners for low footprint network intrusion detection. Complex and Intelligent Systems, 9(4), 3787–3799. https://doi.org/10.1007/s40747-022-00809-3. 2023.
[29] Mahmoud, A., & Takaoka, E. An enhanced machine learning approach with stacking ensemble learner for accurate liver cancer diagnosis using feature selection and gene expression data. Healthcare Analytics, 7. https://doi.org/10.1016/j.health.2024.100373. 2025.
[30] B. B. Özen, F. Karada?, and A. Ba Alawi, “Multi-Model Stacking Ensemble Approach for Improving Oral Cancer Diagnosis,” in 32nd IEEE Conference on Signal Processing and Communications Applications, SIU 2024 - Proceedings, Institute of Electrical and Electronics Engineers Inc. doi: 10.1109/SIU61531.2024.10600983. 2024.
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