{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T04:29:36Z","timestamp":1783398576369,"version":"3.54.6"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,28]],"date-time":"2025-06-28T00:00:00Z","timestamp":1751068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Time series forecasting is critical for decision-making in numerous domains, yet achieving high accuracy across both short-term and long-term horizons remains challenging. In this paper, we propose a general hybrid forecasting framework that integrates a traditional statistical model (ARIMA) with modern deep learning models (such as LSTM and Transformer). The core of our approach is a novel multi-scale prediction mechanism that combines the strengths of both model types to better capture short-range patterns and long-range dependencies. We design a dual-stage forecasting process, where a classical time series component first models transparent linear trends and seasonal patterns, and a deep neural network then learns complex nonlinear residuals and long-term contexts. The two outputs are fused through an adaptive mechanism to produce the final prediction. We evaluate the proposed framework on eight public datasets (electricity, exchange rate, weather, traffic, illness, ETTh1\/2, and ETTm1\/2) covering diverse domains and scales. The experimental results show that our hybrid method consistently outperforms stand-alone models (ARIMA, LSTM, and Transformer) and recent, specialized forecasters (Informer and Autoformer) in both short-horizon and long-horizon forecasts. An ablation study further demonstrates the contribution of each module in the framework. The proposed approach not only achieves state-of-the-art accuracy across varied time series but also offers improved interpretability and robustness, suggesting a promising direction for combining statistical and deep learning techniques in time series forecasting.<\/jats:p>","DOI":"10.3390\/e27070695","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T07:42:06Z","timestamp":1751355726000},"page":"695","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["A Hybrid Framework Integrating Traditional Models and Deep Learning for Multi-Scale Time Series Forecasting"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4996-5130","authenticated-orcid":false,"given":"Zihan","family":"Liu","sequence":"first","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, 219 Ningliu Road, Nanjing 210044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zijia","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, 219 Ningliu Road, Nanjing 210044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weizhe","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, 219 Ningliu Road, Nanjing 210044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lai, G., Chang, W.C., Yang, Y., and Liu, H. (2018, January 8\u201312). Modeling long-and short-term temporal patterns with deep neural networks. Proceedings of the 41st International ACM SIGIR Conference on Research & Development in Information Retrieval, Ann Arbor, MI, USA.","DOI":"10.1145\/3209978.3210006"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1109\/TON.2025.3526148","article-title":"Prioritized Information Bottleneck Theoretic Framework With Distributed Online Learning for Edge Video Analytics","volume":"33","author":"Fang","year":"2025","journal-title":"IEEE Trans. Netw."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1002\/hcs2.123","article-title":"A novel ensemble ARIMA-LSTM approach for evaluating COVID-19 cases and future outbreak preparedness","volume":"3","author":"Jain","year":"2024","journal-title":"Health Care Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lea, C., Flynn, M.D., Vidal, R., Reiter, A., and Hager, G.D. (2017, January 21\u201326). Temporal convolutional networks for action segmentation and detection. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.113"},{"key":"ref_6","unstructured":"Lea, C., Vidal, R., Reiter, A., and Hager, G.D. (15\u201316, January 8\u201310). Temporal convolutional networks: A unified approach to action segmentation. Proceedings of the Computer Vision\u2014ECCV 2016 Workshops, Amsterdam, The Netherlands. Part III 14."},{"key":"ref_7","first-page":"042050","article-title":"Temporal convolutional networks for anomaly detection in time series","volume":"Volume 1213","author":"He","year":"2019","journal-title":"Proceedings of the Journal of Physics: Conference Series"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wu, B., Huang, J., and Duan, Q. (2025). Real-time Intelligent Healthcare Enabled by Federated Digital Twins with AoI Optimization. IEEE Netw., in press.","DOI":"10.1109\/MNET.2025.3565977"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6350647","DOI":"10.1155\/2023\/6350647","article-title":"Model-Free Cooperative Optimal Output Regulation for Linear Discrete-Time Multi-Agent Systems Using Reinforcement Learning","volume":"2023","author":"Wu","year":"2023","journal-title":"Math. Probl. Eng."},{"key":"ref_10","unstructured":"Barrenetxea, M., and Lopez Erauskin, R. (2023, January 4\u20138). Comparison between the ETT and LTT Technologies for Electronic OLTC Transformer Applications. Proceedings of the 2023 25th European Conference on Power Electronics and Applications (EPE\u201923 ECCE Europe), Aalborg, Denmark."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Huang, J., Wu, B., Duan, Q., Dong, L., and Yu, S. (2025). A Fast UAV Trajectory Planning Framework in RIS-assisted Communication Systems with Accelerated Learning via Multithreading and Federating. IEEE Trans. Mob. Comput., in press.","DOI":"10.1109\/TMC.2025.3544903"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1162\/003465301750160054","article-title":"Long-horizon exchange rate predictability?","volume":"83","author":"Berkowitz","year":"2001","journal-title":"Rev. Econ. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"58","DOI":"10.5430\/irhe.v4n3p58","article-title":"The impact of lengths of time series on the accuracy of the ARIMA forecasting","volume":"4","author":"Qin","year":"2019","journal-title":"Int. Res. High. Educ."},{"key":"ref_14","unstructured":"Redd, A., Khin, K., and Marini, A. (2019). Fast es-rnn: A gpu implementation of the es-rnn algorithm. arXiv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"81180","DOI":"10.1109\/ACCESS.2023.3299340","article-title":"AoI-aware resource management for smart health via deep reinforcement learning","volume":"11","author":"Wu","year":"2023","journal-title":"IEEE Access"},{"key":"ref_16","unstructured":"Fang, Z., Wang, J., Ma, Y., Tao, Y., Deng, Y., Chen, X., and Fang, Y. (2025). R-ACP: Real-Time Adaptive Collaborative Perception Leveraging Robust Task-Oriented Communications. arXiv."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, H., Chen, J., Zheng, A., Wu, Y., and Luo, Y. (2024, January 16\u201322). Day-Night Cross-domain Vehicle Re-identification. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR52733.2024.01200"},{"key":"ref_18","unstructured":"Bai, S., Kolter, J.Z., and Koltun, V. (2018). An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling. arXiv."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., and Zhang, W. (2021, January 2\u20139). Informer: Beyond efficient transformer for long sequence time-series forecasting. Proceedings of the AAAI Conference on Artificial Intelligence.","DOI":"10.1609\/aaai.v35i12.17325"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wu, B., Huang, J., and Duan, Q. (2025, January 24\u201326). FedTD3: An Accelerated Learning Approach for UAV Trajectory Planning. Proceedings of the International Conference on Wireless Artificial Intelligent Computing Systems and Applications (WASA), Tokyo, Japan.","DOI":"10.1007\/978-981-96-8725-1_2"},{"key":"ref_21","first-page":"22419","article-title":"Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting","volume":"34","author":"Wu","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_22","unstructured":"Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., and Jin, R. (2022, January 17\u201323). Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. Proceedings of the International Conference on Machine Learning, PMLR, Baltimore, MD, USA."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zhu, Q., Han, J., Chai, K., and Zhao, C. (2023). Time series analysis based on informer algorithms: A survey. Symmetry, 15.","DOI":"10.3390\/sym15040951"},{"key":"ref_24","first-page":"100827","article-title":"A fault-tolerant and energy-efficient design of a network switch based on a quantum-based nano-communication technique","volume":"37","author":"Pan","year":"2023","journal-title":"Sustain. Comput. Inform. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"108650","DOI":"10.1016\/j.istruc.2025.108650","article-title":"Data-driven wind-induced response prediction for slender civil infrastructure: Progress, challenges and opportunities","volume":"74","author":"Zhang","year":"2025","journal-title":"Structures"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Sina, L.B., Secco, C.A., Blazevic, M., and Nazemi, K. (2023). Hybrid Forecasting Methods\u2014A Systematic Review. Electronics, 12.","DOI":"10.3390\/electronics12092019"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Amreen, S., Panigrahi, R., and Patne, N.R. (2023, January 15\u201317). Solar Power Forecasting Using Hybrid Model. Proceedings of the 2023 5th International Conference on Energy, Power and Environment: Towards Flexible Green Energy Technologies (ICEPE), Shillong, India.","DOI":"10.1109\/ICEPE57949.2023.10201483"},{"key":"ref_28","first-page":"112","article-title":"Hybrid forecasting of geopolitical events","volume":"44","author":"Benjamin","year":"2023","journal-title":"AI Mag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1002\/sres.2179","article-title":"An ARIMA-ANN Hybrid Model for Time Series Forecasting","volume":"30","author":"Li","year":"2013","journal-title":"Syst. Res. Behav. Sci."},{"key":"ref_30","first-page":"e6976","article-title":"Time series forecasting using deep learning hybrid model (ARIMA-LSTM)","volume":"5","author":"Gasmi","year":"2024","journal-title":"Stud. Eng. Exact Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Souto, H.G., and Moradi, A. (2024). Can Transformers Transform Financial Forecasting?. SSRN Electron. J.","DOI":"10.1108\/CFRI-01-2024-0032"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zuo, C., Deng, S., Wang, J., Liu, M., and Wang, Q. (2023). An Ensemble Framework for Short-Term Load Forecasting Based on TimesNet and TCN. Energies, 16.","DOI":"10.3390\/en16145330"},{"key":"ref_33","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, L., and Polosukhin, I. (2023). Attention Is All You Need. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1016\/j.ijforecast.2019.07.001","article-title":"DeepAR: Probabilistic forecasting with autoregressive recurrent networks","volume":"36","author":"Salinas","year":"2020","journal-title":"Int. J. Forecast."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/695\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:00:56Z","timestamp":1760032856000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/7\/695"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,28]]},"references-count":34,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["e27070695"],"URL":"https:\/\/doi.org\/10.3390\/e27070695","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,28]]}}}