Abstract :

This paper presents a hybrid ARIMA–machine learning (ARIMA–ML) regression framework designed to improve predictive accuracy in cyber‑physical systems (CPS). The approach brings together the strengths of classical statistical time‑series modelling and modern data‑driven techniques, allowing the model to capture both linear structures and nonlinear dynamics that commonly arise in CPS environments. A simulation‑based evaluation was conducted using a multivariate dataset generated from a MATLAB/Simulink CPS model, complemented by Python‑based machine learning components. The results show that the hybrid model consistently outperforms standalone ARIMA and ML approaches across multiple operational scenarios, including normal operation, peak load, and early‑stage failure conditions. Improvements were observed not only in RMSE and MAE but also in residual stability, prediction interval reliability, and statistical significance as confirmed by the Diebold–Mariano test. These findings suggest that hybrid modelling offers a practical and effective pathway for enhancing predictive maintenance, anomaly detection, and decision‑support capabilities in complex CPS environments. Future work will explore real‑time deployment, integration with edge computing platforms, and the use of more advanced learning architectures to further strengthen model adaptability and performance.

---

Keywords :

ARIMA–ML integration, Cyber physical systems, Hybrid forecasting models, predictive maintenance, Simulation based evaluation.

---

References :

1. Boichenko, E., Panchenko, A., Tyndyk, M., Maydin, M., Kruglov, S., Artyushenko, V., & Kirsanov, D. (2022). Validation of classification models in cancer studies using simulated spectral data: A “sandbox” concept. Chemometrics and Intelligent Laboratory Systems, 225, 104564. https://doi.org/10.1016/j.chemolab.2022.104564
2. Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
3. Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.
4. Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press.
5. Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and practice (3rd ed.). OTexts. ISBN-13 ‏ : ‎ 978-0987507136
6. Deter, D., Wang, C., Cook, A., & Perry, N. K. (2021). Simulating the autonomous future: A look at virtual vehicle environments and how to validate simulation using public data sets. IEEE Signal Processing Magazine, 38(1), 111–121. https://doi.org/10.1109/MSP.2020.2984428
7. DiRenzo, G. V., Hanks, E., & Miller, D. A. W. (2023). A practical guide to understanding and validating complex models using data simulations. Methods in Ecology and Evolution, 14, 203–217. https://doi.org/10.1111/2041210X.14030
8. Ivan Belik, P., Bhattacharya, P., & Knudsen, E. S. (2024). A case for simulated data and simulation-based models inorganizational network research. Research Policy, 53(8), 105058. https://doi.org/10.1016/j.respol.2024.105058
9. Guiguet,A., & Pons, D. (2025). A Validation Framework for Bulk Distribution Logistics Simulation Models. Logistics, 9(1), 3. https://doi.org/10.3390/logistics9010003
10. Khan, M. M. H., Muhammad, N. S., & El-Shafie, A. (2020). Wavelet-based hybrid ANN-ARIMA models for meteorological drought forecasting. Journal of Hydrology, 589, 125151.
11. Khashei, M., & Bijari, M. (2011). A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Applied Soft Computing, 11(2), 2664–2675. https://doi.org/10.1016/j.asoc.2010.10.015
12. Here is the correct APA (7th ed.) reference:
13. Kumar, N., & Susan, S. (2020). COVID-19 pandemic prediction using time series forecasting models. In Proceedings of the 11th International Conference on Computing, Communication and Networking Technologies (ICCCNT) (pp. xxx–xxx). IEEE.
14. Lee, E. A., & Seshia, S. A. (2017). Introduction to embedded systems: A cyber‑physical systems approach (2nd ed.). MIT Press.
15. Li, X., & Chen, Y. (2022). Hybrid predictive maintenance modeling for cyber‑physical systems. IEEE Transactions on Industrial Informatics, 18(4), 2561–2572. https://doi.org/10.1109/TII.2021.3139874
16. Marchi, H., Schmiegel, S., Schamberger, T., & Fuchs, C. (2026). Validating methods for inferring co-occurring diseases: a flexible framework for simulating synthetic data. https://doi.org/10.64898/2026.01.13.26344018
17. Nikolov, N. (2025). Assessment of the ecological footprint of smart cities through sustainable development indicators. Annual of Natural Sciences Department, 10, 40–50.
18. Nikolov, N. (2024a). Development of an intelligent system for managing energy consumption in the home. Computer Science and Technologies (Technical University of Varna), 11–20.
19. Nikolov, N. (2024b). Integration of renewable energy systems in the infrastructure of smart cities. Annual of Natural Sciences Department, 9, 44–52. https://doi.org/10.33919/ansd.24.9.5
20. Pai, P.-F., & Lin, C.-S. (2005). A hybrid ARIMA and support vector machines model in stock price forecasting. Omega, 33(6), 497–505. https://doi.org/10.1016/j.omega.2004.07.024
21. Rizvi, M.F. (2024). ARIMA Model Time Series Forecasting. International Journal for Research in Applied Science and Engineering Technology. https://doi.org/10.22214/ijraset.2024.62416
22. Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1(5), 206–215. https://doi.org/10.1038/s42256-019-0048-x
23. Satrio, C. B. A., Darmawan, W., Nadia, B. U., & Hanafiah, N. (2021). Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and Prophet. Procedia Computer Science, 179, 524–532.
24. Venu, V. and Namitha, M.R. (2025). Applications of Auto-regressive Integrated Moving Average (ARIMA) Model in Agricultural Engineering: A Review. Agricultural Reviews. 1-11. https://doi.org/10.18805/ag.R-2780.
25. Wang, Y., & Guo, Y. (2020). Forecasting method of stock market volatility in time series data based on mixed model of ARIMA and XGBoost. China Communications, 17(7), 205–221.
26. Wang, J., & Jiang, C. (2020). Machine learning‑based forecasting for cyber‑physical systems. IEEE Access, 8, 123456–123468.
27. Zhang, G. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159–175. https://doi.org/10.1016/S0925-2312(01)00702-0
28. Zhang, Y., Wang, L., & Liu, H. (2019). Data‑driven predictive modeling in cyber‑physical systems. IEEE Transactions on Automation Science and Engineering, 16(4), 1523–1534. https://doi.org/10.1109/TASE.2018.2877768
29. Zhao, Z., Li, P., & Sun, Y. (2021). Predictive maintenance for CPS using hybrid statistical–machine learning models. Reliability Engineering & System Safety, 210, 107550. https://doi.org/10.1016/j.ress.2021.107550