A Hybrid Prediction Model Using Statistical Forecasters and Deep Neural Networks
Source abstract
Abstract
The ability to accurately predict future time series behavior in multiple steps, known as multi-horizon forecasting, is a vital aspect in various industries, including retail sales, energy consumption, server load, healthcare, weather, and others. We have proposed, in this paper, the use of statistical forecasters as covariates in a Deep Neural Network (DNN) model and evaluated its impact on forecast metrics. Our analysis covered four diverse datasets: M5, Stallion, Stock Market, and Synthetic. The results demonstrated that the inclusion of statistical predictors in the DNN model led to varying degrees of improvement in forecast performance, depending on the dataset and the chosen evaluation metric. In general, our findings suggest that incorporating statistical prediction as a covariate can be a valuable approach to improving multi-horizon prediction, especially in scenarios with data scarcity and intermittency. The hybrid model achieved consistent improvements, particularly on Symmetric Mean Absolute Percentage Error (SMAPE) across datasets, with statistically significant gains on synthetic and stock market series. Specifically, SMAPE was reduced by approximately 33% on synthetic and stock market datasets, by 15–20% on Stallion, and by around 6% on M5. These results confirm that integrating statistical forecasts as covariates can substantially enhance predictive accuracy, especially for volatile or synthetic series.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Forecasting Techniques and Applications · Stock Market Forecasting Methods · Energy Load and Power Forecasting
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Polytechnic School, University of Vale do Itajaí (UNIVALI), Uruguai St. n.458, Itajai 88302-901, SC, Brazil
Faculty of Electrical Engineering, Polytechnic School, Pontifical Catholic University of Campinas, Professor Doutor Euryclides de Jesus Zerbini St. n.1516, Campinas 13087-571, SP, Brazil
Expert Systems and Applications Lab, Faculty of Science, University of Salamanca, Plaza de los Caídos s/n, 37008 Salamanca, Spain
Funding
Foundation for Research and Innovation of the State of Santa Catarina
References (74)
Show source-provided references
1. Wind speed forecasting approach using conformal prediction and feature importance selection10.1016/j.ijepes.2025.110700 ↗
2. Time-series forecasting with deep learning: A survey10.1098/rsta.2020.0209 ↗
3. Lopes, H., Pires, I.M., Sánchez San Blas, H., García-Ovejero, R., and Leithardt, V. (2020). PriADA: Management and Adaptation of Information Based on Data Privacy in Public Environments. Computers, 9.10.3390/computers9040077 ↗
4. Elucidate structure in intermittent demand series10.1016/j.ejor.2020.05.046 ↗
5. Forecasting intermittent demand for inventory management by retailers: A new approach10.1016/j.jretconser.2021.102662 ↗
6. Jain, G., and Mallick, B. (2017). A study of time series models ARIMA and ETS. SSRN Electron. J.10.2139/ssrn.2898968 ↗
7. Automatic time series forecasting: The forecast package for R10.18637/jss.v027.i03 ↗
8. Hyndman, R.J., and Athanasopoulos, G. (2018). Forecasting: Principles and Practice, OTexts.
9. DeepAR: Probabilistic forecasting with autoregressive recurrent networks10.1016/j.ijforecast.2019.07.001 ↗
10. Temporal fusion transformers for interpretable multi-horizon time series forecasting10.1016/j.ijforecast.2021.03.012 ↗
11. Long short-term memory10.1162/neco.1997.9.8.1735 ↗
12. Chevalier, G. (2018). LARNN: Linear attention recurrent neural network. arXiv.
13. Bui, V., Le, N.T., Nguyen, V.H., Kim, J., and Jang, Y.M. (2021). Multi-behavior with bottleneck features LSTM for load forecasting in building energy management system. Electronics, 10.10.3390/electronics10091026 ↗
14. Enhancing hydroelectric inflow prediction in the Brazilian power system: A comparative analysis of machine learning models and hyperparameter optimization for decision support10.1016/j.epsr.2024.110275 ↗
15. Klaar, A.C.R., Stefenon, S.F., Seman, L.O., Mariani, V.C., and Coelho, L.S. (2023). Optimized EWT-Seq2Seq-LSTM with attention mechanism to insulators fault prediction. Sensors, 23.10.3390/s23063202 ↗
16. Hypertuned temporal fusion transformer for multi-horizon time series forecasting of dam level in hydroelectric power plants10.1016/j.ijepes.2024.109876 ↗
17. Spatiotemporal wind energy forecasting: A comprehensive survey and a deep equilibrium-based case study with StemGNN10.1109/ACCESS.2025.3586997 ↗
18. Artificial neural networks (the multilayer perceptron)—A review of applications in the atmospheric sciences10.1016/S1352-2310(97)00447-0 ↗
19. The levenberg-marquardt algorithm
20. Neural Hierarchical Interpolation Time Series (NHITS) for Reservoir Level Multi-Horizon Forecasting in Hydroelectric Power Plants10.1109/ACCESS.2025.3554446 ↗
21. An overview of performance evaluation metrics for short-term statistical wind power forecasting10.1016/j.rser.2020.110515 ↗
22. Akiba, T., Sano, S., Yanase, T., Ohta, T., and Koyama, M. (2019, January 4–8). Optuna: A next-generation hyperparameter optimization framework. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.10.1145/3292500.3330701 ↗
23. Branco, N.W., Cavalca, M.S.M., Stefenon, S.F., and Leithardt, V.R.Q. (2022). Wavelet LSTM for Fault Forecasting in Electrical Power Grids. Sensors, 22.10.20944/preprints202210.0004.v1 ↗
24. A hybrid method of exponential smoothing and recurrent neural networks for time series forecasting10.1016/j.ijforecast.2019.03.017 ↗
25. Photovoltaic power forecasting using wavelet neuro-fuzzy for active solar trackers
26. Ensemble learning methods using the Hodrick–Prescott filter for fault forecasting in insulators of the electrical power grids10.1016/j.ijepes.2023.109269 ↗
27. Box, G., and Jenkins, G. (1976). Analysis: Forecasting and Control, Holden Day.
28. Hyndman, R., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008). Forecasting with Exponential Smoothing: The State Space Approach, Springer Science & Business Media.10.1007/978-3-540-71918-2 ↗
29. Forecasting and stock control for intermittent demands10.1057/jors.1972.50 ↗
30. The accuracy of intermittent demand estimates10.1016/j.ijforecast.2004.10.001 ↗
31. Forecast reconciliation: A geometric view with new insights on bias correction10.1016/j.ijforecast.2020.06.004 ↗
32. Forecasting at scale10.1080/00031305.2017.1380080 ↗
33. The M4 Competition: Results, findings, conclusion and way forward10.1016/j.ijforecast.2018.06.001 ↗
34. Forecasting in social settings: The state of the art10.1016/j.ijforecast.2019.05.011 ↗
35. The M5 competition: Background, organization, and implementation10.1016/j.ijforecast.2021.07.007 ↗
36. Wavelet-Seq2Seq-LSTM with attention for time series forecasting of level of dams in hydroelectric power plants10.1016/j.energy.2023.127350 ↗
37. What is the best RNN-cell structure to forecast each time series behavior?10.1016/j.eswa.2022.119140 ↗
38. Fault diagnosis of insulators from ultrasound detection using neural networks
39. Stefenon, S.F., Singh, G., Yow, K.C., and Cimatti, A. (2022). Semi-ProtoPNet deep neural network for the classification of defective power grid distribution structures. Sensors, 22.10.3390/s22134859 ↗
40. Starke, L., Hoppe, A.F., Sartori, A., Stefenon, S.F., Santana, J.F.D.P., and Leithardt, V.R.Q. (2023). Interference recommendation for the pump sizing process in progressive cavity pumps using graph neural networks. Sci. Rep., 13.10.1038/s41598-023-43972-4 ↗
41. Hypertuned-YOLO for interpretable distribution power grid fault location based on EigenCAM10.1016/j.asej.2024.102722 ↗
42. Enhanced insulator fault detection using optimized ensemble of deep learning models based on weighted boxes fusion10.1016/j.ijepes.2025.110682 ↗
43. Salazar, L.H.A., Leithardt, V.R.Q., Parreira, W.D., da Rocha Fernandes, A.M., Barbosa, J.L.V., and Correia, S.D. (2022). Application of Machine Learning Techniques to Predict a Patient’s No-Show in the Healthcare Sector. Future Internet, 14.10.3390/fi14010003 ↗
44. Long short-term memory stacking model to predict the number of cases and deaths caused by COVID-19
45. Low-Cost CNN for Automatic Violence Recognition on Embedded System10.1109/ACCESS.2022.3155123 ↗
46. Enhanced multi-step streamflow series forecasting using hybrid signal decomposition and optimized reservoir computing models10.1016/j.eswa.2024.124856 ↗
47. Variational mode decomposition and bagging extreme learning machine with multi-objective optimization for wind power forecasting10.1007/s10489-024-05331-2 ↗
48. Stefenon, S.F., Seman, L.O., Schutel Furtado Neto, C., Nied, A., Seganfredo, D.M., Garcia da Luz, F., Sabino, P.H., Torreblanca González, J., and Quietinho Leithardt, V.R. (2020). Electric field evaluation using the finite element method and proxy models for the design of stator slots in a permanent magnet synchronous motor. Electronics, 9.10.3390/electronics9111975 ↗
49. Automatic digitalization of railway interlocking systems engineering drawings based on hybrid machine learning methods10.1016/j.eswa.2025.127532 ↗
50. Analysis of the ultrasonic signal in polymeric contaminated insulators through ensemble learning methods10.1109/ACCESS.2022.3161506 ↗
51. Oreshkin, B.N., Carpov, D., Chapados, N., and Bengio, Y. (2020, January 26–30). N-BEATS: Neural basis expansion analysis for interpretable time series forecasting. Proceedings of the VIII International Conference on Learning Representations, Addis Ababa, Ethiopia.
52. Challu, C., Olivares, K.G., Oreshkin, B.N., Ramirez, F.G., Canseco, M.M., and Dubrawski, A. (2023, January 7–14). Nhits: Neural hierarchical interpolation for time series forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA.10.1609/aaai.v37i6.25854 ↗
53. Evaluation of visible contamination on power grid insulators using convolutional neural networks10.1007/s00202-023-01915-2 ↗
54. Baldi, P., and Sadowski, P.J. (2013). Understanding dropout. Advances in Neural Information Processing Systems, Curran Associates, Inc.
55. Gal, Y., and Ghahramani, Z. (2016, January 19–24). Dropout as a bayesian approximation: Representing model uncertainty in deep learning. Proceedings of the International Conference on Machine Learning, PMLR, New York, NY, USA.
56. Hybrid wavelet stacking ensemble model for insulators contamination forecasting10.1109/ACCESS.2021.3076410 ↗
57. Javeri, I.Y., Toutiaee, M., Arpinar, I.B., Miller, J.A., and Miller, T.W. (2021, January 23–26). Improving Neural Networks for Time-Series Forecasting using Data Augmentation and AutoML. Proceedings of the 2021 IEEE Seventh International Conference on Big Data Computing Service and Applications (BigDataService), Oxford, UK.10.1109/BigDataService52369.2021.00006 ↗
58. Hypertuned wavelet convolutional neural network with long short-term memory for time series forecasting in hydroelectric power plants10.1016/j.energy.2024.133918 ↗
59. Scikit-learn: Machine Learning in Python
60. Garza, F., Max Mergenthaler Canseco, C.C., and Olivares, K.G. (2022). StatsForecast: Lightning Fast Forecasting with Statistical and Econometric Models, PyCon.
61. Box, G.E., Jenkins, G.M., Reinsel, G.C., and Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control, John Wiley & Sons.
62. Automated multi-model deep neural network for sleep stage scoring with unfiltered clinical data10.1007/s11325-019-02008-w ↗
63. Dubey, A.K., and Jain, V. (2019). Comparative study of convolution neural network’s relu and leaky-relu activation functions. Applications of Computing, Automation and Wireless Systems in Electrical Engineering: Proceedings of MARC 2018, Springer.10.1007/978-981-13-6772-4_76 ↗
64. Deep learning10.1038/nature14539 ↗
65. Borré, A., Seman, L.O., Camponogara, E., Stefenon, S.F., Mariani, V.C., and Coelho, L.S. (2023). Machine fault detection using a hybrid CNN-LSTM attention-based model. Sensors, 23.10.3390/s23094512 ↗
66. dos Santos, G.H., Seman, L.O., Bezerra, E.A., Leithardt, V.R.Q., Mendes, A.S., and Stefenon, S.F. (2021). Static attitude determination using convolutional neural networks. Sensors, 21.10.3390/s21196419 ↗
67. Nagi, J., Ducatelle, F., Di Caro, G.A., Cireşan, D., Meier, U., Giusti, A., Nagi, F., Schmidhuber, J., and Gambardella, L.M. (2011, January 16–18). Max-pooling convolutional neural networks for vision-based hand gesture recognition. Proceedings of the 2011 IEEE International Conference on Signal and Image Processing Applications (ICSIPA), Kuala Lumpur, Malaysia.10.1109/ICSIPA.2011.6144164 ↗
68. Accuracy measures: Theoretical and practical concerns10.1016/0169-2070(93)90079-3 ↗
69. An approach for sales forecasting10.1016/j.eswa.2022.118043 ↗
70. Montgomery, D.C., and Runger, G.C. (2020). Applied Statistics and Probability for Engineers, John Wiley & Sons.
71. The ASA statement on p-values: Context, process, and purpose10.1080/00031305.2016.1154108 ↗
72. Toward evidence-based medical statistics. 1: The P value fallacy10.7326/0003-4819-130-12-199906150-00008 ↗
73. The p-value fallacy and how to avoid it10.1037/h0087425 ↗
74. Are the fallacies of the P value finally ended?10.21037/jtd.2016.04.48 ↗