Comparative Evaluation of Statistical and Deep Learning Models for Multi-Product Sales Forecasting
DOI:
https://doi.org/10.15294/edukom.v12i2.39797Keywords:
Adaptive Ensemble, Deep Learning, Multi-Product Forecasting, Time SeriesAbstract
Sales forecasting plays a crucial role in retail decision-making, particularly in multi-product environments with heterogeneous demand characteristics. Unlike most previous studies that focus on finding a single best model globally, this study conducts a standardized comparative evaluation between statistical (TES, SARIMA) and deep learning (LSTM, CNN–LSTM) models using six years of real retail sales data covering eight products with stable seasonal patterns to volatile and nonlinear demand, thus representing the complexity of retail scenarios. To ensure the validity and reliability of the evaluation, data leakage was prevented by splitting the data seasonally (80% training, 20% testing), applying all transformations (scaling, log transform, sequence generation) estimated only on the training data, and using a consistent multi-step autoregressive scheme across all models. Model performance was evaluated using MAPE, MAE, MSE, and RMSE. The adaptive ensemble strategy was implemented by combining SARIMA and CNN–LSTM through optimization of product-specific weights (α ∈ [0,1], interval 0.01) using grid search to minimize MAPE over the testing horizon. The results show that the deep learning model outperforms products with fluctuating and nonlinear demand, while the statistical model remains competitive on products with stable seasonal patterns. Aggregated across products, the adaptive ensemble yielded the lowest average MAPE (0.2184), lower than all individual models, indicating better stability in the face of demand heterogeneity. This study confirms the product-dependent nature of forecasting performance and offers a replicable adaptive framework for multi-product forecasting. By enhancing data-driven supply chain efficiency and supporting skill development in advanced forecasting methodologies, this research aligns with Sustainable Development Goals (SDG) 8 and SDG 4.
References
Amalou, I., Mouhni, N., & Abdali, A. (2024). CNN-LSTM architectures for non-stationary time series: decomposition approach. 2024 International Conference on Global Aeronautical Engineering and Satellite Technology (GAST), 1–5. https://doi.org/10.1109/GAST60528.2024.10520774
Arratia, A., El Daou, M., Kagerhuber, J., & Smolyarova, Y. (2025). Examining Challenges in Implied Volatility Forecasting: A Critical Review of Data Leakage and Feature Engineering combined with High-Complexity Models. Computational Economics. https://doi.org/10.1007/s10614-025-11172-z
Aswini, K., Reddy, U., Nagpal, A., Rana, A., Praveen, & Abood, B. S. Z. (2023). Ensemble Learning Approaches for Big Data Classification Tasks. 2023 10th IEEE Uttar Pradesh Section International Conference on Electrical, Electronics and Computer Engineering (UPCON), 10, 1545–1550. https://doi.org/10.1109/UPCON59197.2023.10434616
Boukrouh, I., Idiri, S., Tayalati, F., Azmani, A., & Bouhsaien, L. (2025). A Hybrid Approach for Sales Forecasting: Combining Deep Learning and Time Series Analysis. International Journal of Engineering, Transactions A: Basics, 38(4), 859–870. https://doi.org/10.5829/ije.2025.38.04a.16
Cerqueira, V., Roque, L., & Soares, C. (2025a). Forecasting with Deep Learning: Beyond Average of Average of Average Performance. In D. Pedreschi, A. Monreale, R. Guidotti, R. Pellungrini, & F. Naretto (Eds.), Discovery Science (pp. 135–149). Springer Nature Switzerland.
Cerqueira, V., Roque, L., & Soares, C. (2025b). Forecasting with Deep Learning: Beyond Average of Average of Average Performance. In D. Pedreschi, A. Monreale, R. Guidotti, R. Pellungrini, & F. Naretto (Eds.), Discovery Science (pp. 135–149). Springer Nature Switzerland.
Chen, J. (2025). Research on the Construction of Short-Term Demand Forecasting Model of Express Logistics Based on Deep Learning. 2025 5th International Conference on Artificial Intelligence, Big Data and Algorithms (CAIBDA), 406–409. https://doi.org/10.1109/CAIBDA65784.2025.11183456
de Castro Moraes, T., Yuan, X. M., & Chew, E. P. (2024a). Hybrid convolutional long short-term memory models for sales forecasting in retail. Journal of Forecasting, 43(5), 1278–1293. https://doi.org/10.1002/for.3073
de Castro Moraes, T., Yuan, X. M., & Chew, E. P. (2024b). Hybrid convolutional long short-term memory models for sales forecasting in retail. Journal of Forecasting, 43(5), 1278–1293. https://doi.org/10.1002/for.3073
Eglite, L., & Birzniece, I. (2022). Retail Sales Forecasting Using Deep Learning: Systematic Literature Review. Complex Systems Informatics and Modeling Quarterly, 2022(30), 53–62. https://doi.org/10.7250/csimq.2022-30.03
Hammam, I. M., El-Kharbotly, A. K., & Sadek, Y. M. (2025). Adaptive demand forecasting framework with weighted ensemble of regression and machine learning models along life cycle variability. Scientific Reports, 15(1). https://doi.org/10.1038/s41598-025-23352-w
Hasan, P., Khan, T. D., Abedin, M., & Haque, M. E. (2025). Temporal trends and forecasting of respiratory mortality in Bangladesh: A SARIMA model for seasonal mortality risk and public health action. Journal of Public Health Research, 14(4). https://doi.org/10.1177/22799036251395248
Hewage, H. C., Perera, H. N., & Bandara, K. (2025). Enhancing Demand Forecasting in Retail: A Comprehensive Analysis of Sales Promotional Effects on the Entire Demand Life Cycle. Journal of Forecasting. https://doi.org/10.1002/for.70039
Huang, S., & Zhou, L. (2025). A Residual-Corrected Hybrid ARIMA–CNN–LSTM Framework for High-Accuracy Tobacco Sales Forecasting in Regulated Markets. International Journal of Computational Intelligence Systems, 18(1). https://doi.org/10.1007/s44196-025-00930-4
Jouilil, Y., & Iaousse, M. (2023). Comparing the Accuracy of Classical, Machine Learning, and Deep Learning Methods in Time Series Forecasting: A Case Study of USA Inflation. Statistics, Optimization and Information Computing, 11(4), 1041–1050. https://doi.org/10.19139/soic-2310-5070-1767
Kristianto, R. P., & Setyanto, A. (2018). Golden Section Search-Multi Variable Algorithm for Optimization Parameter of Triple Exponential Smoothing Algorithm to Predict Sufferers of Lungs Disease. 2018 3rd International Conference on Information Technology, Information System and Electrical Engineering (ICITISEE), 194–198. https://doi.org/10.1109/ICITISEE.2018.8720967
Kumari, P., & Toshniwal, D. (2021). Long short term memory–convolutional neural network based deep hybrid approach for solar irradiance forecasting. Applied Energy, 295, 117061. https://doi.org/10.1016/J.APENERGY.2021.117061
Lawal, Y. B., Owolawi, P. A., Tu, C., Van Wyk, E., & Ojo, J. S. (2024). Stochastic Dynamical Modeling for Time-series Zero-Degree Isotherm Heights Prediction over Tropical Climate. IOP Conference Series: Earth and Environmental Science, 1428(1). https://doi.org/10.1088/1755-1315/1428/1/012017
Nakthanom, S. (2025). Using Long Short-Term Memory to Losses Prediction for Three-Phase Distribution Transformer. 2025 International Technical Conference on Circuits/Systems, Computers, and Communications (ITC-CSCC), 1–8. https://doi.org/10.1109/ITC-CSCC66376.2025.11137634
Osman, E. G. A., & Otaibi, F. A. (2025). Integrating deep learning and econometrics for stock price prediction: A comprehensive comparison of LSTM, transformers, and traditional time series models. Machine Learning with Applications, 22, 100730. https://doi.org/10.1016/j.mlwa.2025.100730
Pongdatu, G. A. N., & Putra, Y. H. (2018). Seasonal Time Series Forecasting using SARIMA and Holt Winter’s Exponential Smoothing. IOP Conference Series: Materials Science and Engineering, 407(1). https://doi.org/10.1088/1757-899X/407/1/012153
Popovska, E., & Georgieva-Tsaneva, G. (2024). Comparative Analysis of ARIMA and LSTM Models for Seasonal Times-Series Forecasting. 2024 15th National Conference with International Participation (ELECTRONICA), 1–3. https://doi.org/10.1109/ELECTRONICA63645.2024.11146090
Ram, C. S., Raj, M., & Chaturvedi, R. K. (2025). Boosting Time-Series Forecasting Accuracy with SARIMAX Seasonal Interval Automation. Procedia Computer Science, 260, 814–821. https://doi.org/10.1016/j.procs.2025.03.262
Rygh, T., Vaage, C., Westgaard, S., & Lange, P. E. de. (2025). Inflation Forecasting: LSTM Networks vs. Traditional Models for Accurate Predictions. Journal of Risk and Financial Management, 18(7). https://doi.org/10.3390/jrfm18070365
Ryu, K., Jang, S. S., & Sanchez, A. (2003). Forecasting Methods and Seasonal Adjustment for a University Foodservice Operation. Journal of Foodservice Business Research, 6(2), 17–34. https://doi.org/10.1300/J369v06n02_03
Selmy, H. A., Mohamed, H. K., & Medhat, W. (2024). A predictive analytics framework for sensor data using time series and deep learning techniques. Neural Computing and Applications, 36(11), 6119–6132. https://doi.org/10.1007/s00521-023-09398-9
Shan, K., Wang, Y., Tang, Z., Chen, Y., & Li, Y. (2021). MixTConv: Mixed Temporal Convolutional Kernels for Efficient Action Recognition. 2020 25th International Conference on Pattern Recognition (ICPR), 1751–1756. https://doi.org/10.1109/ICPR48806.2021.9412586
Sooriarachchi, S. R., Hettiarachchi, G. P., & Dharmarathne, G. (2026). Deep Learning Models for Multimodal Demand Forecasting in Retail: A Comparative Case Study of Long Short-Term Memory and Temporal Fusion Transformers. In C. Anutariya, M. Bonsangue, A. Pinidiyaarachchi, & H. Usoof (Eds.), Data Science and Artificial Intelligence (pp. 195–206). Springer Nature Singapore.
Strøm, E., & Gundersen, O. E. (2024). Performance metrics for multi-step forecasting measuring win-loss, seasonal variance and forecast stability: an empirical study. Applied Intelligence, 54(21), 10490–10515. https://doi.org/10.1007/s10489-024-05715-4
Taylor, J. W., & McSharry, P. E. (2017). Univariate Methods for Short‐Term Load Forecasting. In Advances in Electric Power and Energy Systems (pp. 17–40). Wiley. https://doi.org/10.1002/9781119260295.ch2
Wang, S., Lin, Y., Jia, Y., Sun, J., & Yang, Z. (2024). Unveiling the Multi-Dimensional Spatio-Temporal Fusion Transformer (MDSTFT): A Revolutionary Deep Learning Framework for Enhanced Multi-Variate Time Series Forecasting. IEEE Access, 12, 115895–115904. https://doi.org/10.1109/ACCESS.2024.3444788
Xue, N., Triguero, I., Figueredo, G. P., & Landa-Silva, D. (2019). Evolving Deep CNN-LSTMs for Inventory Time Series Prediction. 2019 IEEE Congress on Evolutionary Computation (CEC), 1517–1524. https://doi.org/10.1109/CEC.2019.8789957
Zhou, S., Guo, S., Du, B., Huang, S., & Guo, J. (2022). A Hybrid Framework for Multivariate Time Series Forecasting of Daily Urban Water Demand Using Attention-Based Convolutional Neural Network and Long Short-Term Memory Network. Sustainability (Switzerland), 14(17). https://doi.org/10.3390/su141711086
