Hybrid Transformer-TCN Forecasting with Time-Aware Conformal Prediction for Multi-Horizon Uncertainty and Decision Support
DOI:
https://doi.org/10.62007/joumi.v4i1.672Keywords:
time-series forecasting, transformer, temporal convolutional network, conformal prediction, prediction intervalsAbstract
Multivariate time-series forecasting is widely deployed in energy and industrial moni toring, where non-stationarity and distribution shift make point forecasts insufficient for risk-aware decisions. This paper studies multi-horizon forecasting on the ETTh1 benchmark (target OT) and addresses two practical problems: (i) combining local pattern extraction and long-range dependency modeling in a single forecaster, and (ii) producing reliable uncertainty that remains useful under temporal drift. We propose a hybrid architecture that applies a causal dilated Temporal Convolutional Network (TCN) to capture local dynamics and then refines representations with a Transformer encoder for long dependencies, predicting horizons {96,192,336,720} with a shared head. For uncertainty, we apply time-aware conformal prediction under a chronological evaluation protocol to produce multi-horizon prediction intervals at a user-chosen miscoverage level. We compare static conformal calibration with rolling-window calibration and analyze the width–coverage tradeoff. Empirically, rolling calibration increases mean test coverage from 0.671 to 0.758 and improves shift coverage from 0.630 to 0.666, at the cost of a wider mean interval (15.310 to 16.323). Finally, we connect uncertainty to operational use by defining interval-aware alert rules and reporting false-positive/recall tradeoffs, illustrating how interval policies can be tuned to different risk tolerances. Overall, the proposed hybrid forecaster with time-aware conformal calibra tion provides a simple, modular approach to multi-horizon forecasting with interpretable uncertainty and measurable reliability gains under temporal shift.
References
Abdar, M., Pourpanah, F., Hussain, S., Rezazadegan, D., Liu, L., Ghavamzadeh, M., Fieguth, P., Cao, X., Khosravi, A., Acharya, U. R., Makarenkov, V., & Nahavandi, S. (2021). A review of uncertainty quantification in deep learning: Techniques, applications and challenges. Information Fusion, 76, 243–297. https://doi.org/10.1016/j.inffus.2021.05.008
Angelopoulos, A. N., & Bates, S. (2023). Conformal prediction: A gentle introduction. Foundations and Trends in Machine Learning, 16(4), 494–591. https://doi.org/10.1561/2200000101
Benidis, K., Rangapuram, S. S., Flunkert, V., Wang, Y., Maddix, D., Turkmen, C., Gasthaus, J., et al. (2022). Deep learning for time series forecasting: Tutorial and literature survey. ACM Computing Surveys. https://doi.org/10.1145/3533382
Danang, D., & Mustofa, Z. (2026). CLSTMNet architecture: A CNN-LSTM-based hybrid deep learning model for DDoS attack detection and mitigation in network security. Journal of Artificial Intelligence and Technology.
Danang, D., Wahyono, T., Sembiring, I., Wellem, T., & Dzulkefly, N. H. (2025, August). An adaptive framework integrating ML, blockchain, and TEE for cloud security. In 2025 4th International Conference on Creative Communication and Innovative Technology (ICCIT) (pp. 1-7). IEEE.
Kim, D.-K., & Kim, K. (2022). A convolutional transformer model for multivariate time series prediction. IEEE Access, 10, 101319–101329. https://doi.org/10.1109/ACCESS.2022. 3203416
Lara-Benítez, P., Carranza-García, M., & Riquelme, J. C. (2020). Temporal convolutional networks applied to energy-related time series forecasting. Applied Sciences, 10(7), 2322. https://doi.org/10.3390/app10072322
Lara-Benítez, P., Carranza-García, M., & Riquelme, J. C. (2021). Deep learning for time series forecasting: A survey. International Journal of Neural Systems, 31(11), 2130001. https://doi.org/10.1142/S0129065721300011
Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018). Distribution free predictive inference for regression. Journal of the American Statistical Association, 113(523), 1094–1111. https://doi.org/10.1080/01621459.2017.1307116
Lim, B., Arik, S. O., Loeff, N., & Pfister, T. (2021). Temporal fusion transformers for interpretable multi-horizon time series forecasting. International Journal of Forecasting, 37(4), 1748 1764. https://doi.org/10.1016/j.ijforecast.2021.03.012
Lim, B., & Zohren, S. (2021). Time-series forecasting with deep learning: A survey. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379(2194), 20200209. https://doi.org/10.1098/rsta.2020.0209
Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2018). Statistical and machine learning forecasting methods: Concerns and ways forward. PLOS ONE, 13(3), e0194889. https: //doi.org/10.1371/journal.pone.0194889
Nie, Y., Nguyen, N., Sinitsin, A., & Kalinec, G. (2023). Time series forecasting with patchtst. International Conference on Learning Representations.
Salinas, D., Flunkert, V., Gasthaus, J., & Januschowski, T. (2020). Deepar: Probabilistic forecasting with autoregressive recurrent networks. International Journal of Forecasting, 36(3), 1181–1191. https://doi.org/10.1016/j.ijforecast.2019.07.001
Sezer, O. B., Gudelek, M. U., & Ozbayoglu, M. B. (2020). Financial time series forecasting with deep learning: A systematic literature review: 2005–2019. Applied Soft Computing, 90, 106181. https://doi.org/10.1016/j.asoc.2020.106181
Sprangers, O., Schelter, S., & de Rijke, M. (2023). Parameter-efficient deep probabilistic fore casting. International Journal of Forecasting, 39(3), 1474–1489. https://doi.org/10.1016/ j.ijforecast.2022.07.006
Siswanto, E., Danang, D., Kusumaningroem, I., & Akhsani, I. (2026). Assessing software architecture resilience using quantitative metrics in cloud native application development environments. Indonesian Journal of Infomatics, 1(1), 11-21.
Su, L., Zuo, X., Li, R., Wang, X., Zhao, H., & Huang, B. (2025). A systematic review for transformer-based long-term series forecasting. Artificial Intelligence Review, 58, 80. https://doi.org/10.1007/s10462-024-11044-2
Taylor, J. W. (2021). Evaluating quantile-bounded and expectile-bounded interval forecasts. International Journal of Forecasting, 37(2), 800–811. https://doi.org/10.1016/j.ijforecast. 2020.09.007 22
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is all you need. Advances in Neural Information Processing Systems.
Waghmare, A., & Ziegel, J. F. (2025). Proper scoring rules. Annual Review of Statistics and Its Application, 12, 339–365. https://doi.org/10.1146/annurev-statistics-042424-050626
Winkler, R. L. (2019). Probability forecasts and their combination: A decision analysis perspective. Decision Analysis, 16(4), 239–253. https://doi.org/10.1287/deca.2019.0391
Wu, H., Xu, J., Wang, J., & Long, M. (2021). Informer: Beyond efficient transformer for long sequence time-series forecasting. Proceedings of the AAAI Conference on Artificial Intelligence.
Xu, T., Barez, F., Zantedeschi, V., Lathuilière, S., & Łukasik, M. (2024). Development, calibration, and validation of conformal prediction intervals for machine learning models. ACS Omega, 9(27), 29478–29490. https://doi.org/10.1021/acsomega.4c02017
Zeng, P., Li, H., Wang, C., et al. (2022). Muformer: A long sequence time-series forecasting model based on modified multi-head attention. Knowledge-Based Systems, 254, 109584. https://doi.org/10.1016/j.knosys.2022.109584
Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., & Zhang, W. (2021). Autoformer: De composition transformers with auto-correlation for long-term series forecasting. Advances in Neural Information Processing Systems.
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