Skip to main content

Advertisement

SpringerLink
Log in

Multi-step-ahead and interval carbon price forecasting using transformer-based hybrid model

  • Research Article
  • Published:
Environmental Science and Pollution Research Aims and scope Submit manuscript

Abstract

Accurate and stable carbon price forecasts serve as a reference for assessing the stability of the carbon market and play a vital role in enhancing investment and operational decisions. However, realizing this goal is still a significant challenge, and researchers usually ignore multi-step-ahead and interval forecasting due to the non-linear and non-stationary characteristics of carbon price series and its complex fluctuation features. In this study, a novel hybrid model for accurately predicting carbon prices is proposed. The proposed model combines multi-step-ahead and interval carbon price forecasting based on the Hampel identifier (HI), time-varying filtering-based empirical mode decomposition (TVFEMD), and transformer model. First, HI identifies and corrects outliers in carbon price. Second, TVFEMD decomposes carbon price into several intrinsic mode functions (imfs) to reduce the non-linear and non-stationarity of carbon price to obtain more regular features in series. Next, these imfs are reconstructed by sample entropy (SE). Subsequently, the orthogonal array tuning method is used to optimize the transformer model’s hyperparameters to obtain the optimal model structure. Finally, after hyperparameter optimization and quantile loss function, the transformer is used to perform multi-step-ahead and interval forecasting on each part of the reconstruction, and the final prediction result is obtained by summing them up. Five pilot carbon trading markets in China were selected as experimental objects to verify the proposed model’s prediction performance. Various benchmark models and evaluation indicators were selected for comparison and analysis. Experimental results show that the proposed HI-TVFEMD-transformer hybrid model achieves an average MAE of 0.6546, 1.3992, 1.6287, and 2.2601 for one-step, three-step, five-step, and ten-step-ahead forecasting, respectively, which significantly outperforms other models. Furthermore, interval forecasts almost always have a PICI above 0.95 at a confidence interval of 0.1, thereby indicating the effectiveness of the hybrid model in describing the uncertainty in the forecasts. Therefore, the proposed hybrid model is a reliable carbon price forecasting tool that can provide a dependable reference for policymakers and investors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7.
Fig. 8
Fig. 9.
Fig. 10.
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data availability

All data analyzed in the duration of this study are included in the supplementary information files and available from the corresponding author upon reasonable request.

References

  • Benz E, Trück S (2009) Modeling the price dynamics of CO2 emission allowances. Energy Econ 31:4–15

    Google Scholar 

  • Bommidi BS, Teeparthi K, Kosana V (2023) Hybrid wind speed forecasting using ICEEMDAN and transformer model with novel loss function. Energy 265:126383

    Google Scholar 

  • Byun SJ, Cho H (2013) Forecasting carbon futures volatility using GARCH models with energy volatilities. Energy Econ 40:207–221

    Google Scholar 

  • Du Y, Chen K, Chen S, Yin K (2022) Prediction of carbon emissions trading price in Fujian province: based on BP neural network model. Front Energy Res 10:939602

    Google Scholar 

  • Fan X, Lv X, Yin J, Tian L, Liang J (2019) Multifractality and market efficiency of carbon emission trading market: analysis using the multifractal detrended fluctuation technique. Appl Energy 251:113333

    Google Scholar 

  • Graves, A. (2013) Generating sequences with recurrent neural networks. arXiv preprint arXiv:1308.0850

  • Han M, Ding L, Zhao X, Kang W (2019) Forecasting carbon prices in the Shenzhen market, China: the role of mixed-frequency factors. Energy 171:69–76

    Google Scholar 

  • Hao Y, Tian C, Wu C (2020) Modelling of carbon price in two real carbon trading markets. J Clean Prod 244:118556

    Google Scholar 

  • He Y, Li H (2018) Probability density forecasting of wind power using quantile regression neural network and kernel density estimation. Energy Convers Manag 164:374–384

    Google Scholar 

  • Huang Y, Dai X, Wang Q, Zhou D (2021) A hybrid model for carbon price forecasting using GARCH and long short-term memory network. Appl Energy 285:116485

    Google Scholar 

  • Li H, Li Z, Mo W (2017) A time varying filter approach for empirical mode decomposition. Signal Process 138:146–158

    Google Scholar 

  • Lim B, Arık SÖ, Loeff N, Pfister T (2021) Temporal fusion transformers for interpretable multi-horizon time series forecasting. Int J Forecast 37:1748–1764

    Google Scholar 

  • Liu H, Shen L (2019) Forecasting carbon price using empirical wavelet transform and gated recurrent unit neural network. Carbon Manag 11:25–37

    CAS  Google Scholar 

  • Lutz BJ, Pigorsch U, Rotfuss W (2013) Nonlinearity in cap-and-trade systems: The EUA price and its fundamentals. Energy Econ 40:222–232

    Google Scholar 

  • Ma B, Zhang T (2020) Single-channel blind source separation for vibration signals based on TVF-EMD and improved SCA. IET Signal Proc 14:259–268

    Google Scholar 

  • Martins, A. F. T. and Fernandez Astudillo, R. (2016) From Softmax to Sparsemax: a sparse model of attention and multi-label classification. arXiv preprint arXiv:1602.02068

  • Meka R, Alaeddini A, Bhaganagar K (2021) A robust deep learning framework for short-term wind power forecast of a full-scale wind farm using atmospheric variables. Energy 221:119759

    Google Scholar 

  • Niu X, Wang J (2019) A combined model based on data preprocessing strategy and multi-objective optimization algorithm for short-term wind speed forecasting. Appl Energy 241:519–539

    Google Scholar 

  • Peters, B., Niculae, V. and Martins, A. F. T. (2019) Sparse sequence-to-sequence models. arXiv preprint arXiv:1905.05702

  • Richman JS, Moorman JR (2000) Physiological time-series analysis using approximate entropy and sample entropy. Am J Phys Heart Circ Phys 278:H2039–H2049

    CAS  Google Scholar 

  • Sun G, Chen T, Wei Z, Sun Y, Zang H, Chen S (2016) A carbon price forecasting model based on variational mode decomposition and spiking neural networks. Energies 9:54

    Google Scholar 

  • Sun S, Jin F, Li H, Li Y (2021) A new hybrid optimization ensemble learning approach for carbon price forecasting. Appl Math Model 97:182–205

    Google Scholar 

  • Sun W, Huang C (2020a) A carbon price prediction model based on secondary decomposition algorithm and optimized back propagation neural network. J Clean Prod 243:118671

    Google Scholar 

  • Sun W, Huang C (2020b) A novel carbon price prediction model combines the secondary decomposition algorithm and the long short-term memory network. Energy 207:118294

    Google Scholar 

  • Sun W, Xu C (2021) Carbon price prediction based on modified wavelet least square support vector machine. Sci Total Environ 754:142052

    CAS  Google Scholar 

  • Sun W, Zhang C (2018) Analysis and forecasting of the carbon price using multi—resolution singular value decomposition and extreme learning machine optimized by adaptive whale optimization algorithm. Appl Energy 231:1354–1371

    Google Scholar 

  • Sun W, Zhang J (2020) Carbon price prediction based on ensemble empirical mode decomposition and extreme learning machine optimized by improved bat algorithm considering energy price factors. Energies 13:3471

    CAS  Google Scholar 

  • Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183–7192

    Google Scholar 

  • Tian C, Hao Y (2020) Point and interval forecasting for carbon price based on an improved analysis-forecast system. Appl Math Model 79:126–144

    Google Scholar 

  • Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L. and Polosukhin, I. (2017) Attention is all you need. arXiv preprint arXiv:1706.03762

  • Wang J, Du P, Hao Y, Ma X, Niu T, Yang W (2020a) An innovative hybrid model based on outlier detection and correction algorithm and heuristic intelligent optimization algorithm for daily air quality index forecasting. J Environ Manag 255:109855

    CAS  Google Scholar 

  • Wang J, Niu X, Zhang L, Lv M (2021) Point and interval prediction for non-ferrous metals based on a hybrid prediction framework. Res Policy 73:102222

    Google Scholar 

  • Wang J, Qiu S (2021) Improved multi-scale deep integration paradigm for point and interval carbon trading price forecasting. Mathematics 9:2595

    Google Scholar 

  • Wang K, Fu W, Chen T, Zhang B, Xiong D, Fang P (2020b) A compound framework for wind speed forecasting based on comprehensive feature selection, quantile regression incorporated into convolutional simplified long short-term memory network and residual error correction. Energy Convers Manag 222:113234

    Google Scholar 

  • Wang Y, Wang Z, Kang X, Luo Y (2022) A novel interpretable model ensemble multivariate fast iterative filtering and temporal fusion transform for carbon price forecasting. Energy Sci Eng 11:1148–1179

    Google Scholar 

  • Wen, Q., Zhou, T., Zhang, C., Chen, W., Ma, Z., Yan, J. and Sun, L. (2022) Transformers in time series: a survey. arXiv preprint arXiv:2202.07125

  • Wen, R., Torkkola, K., Narayanaswamy, B. and Madeka, D. (2017) A multi-horizon quantile recurrent forecaster. arXiv preprint arXiv:1711.11053

  • Wiegreffe, S. and Pinter, Y. (2019) Attention is not not explanation. arXiv preprint arXiv:1908.04626

  • Wu, N., Green, B., Ben, X. and O'Banion, S. (2020) Deep transformer models for time series forecasting: the influenza prevalence case. arXiv preprint arXiv: 2001.08317v08311

  • Wu Z, Huang NE (2004) Ensemble empirical mode decomposition: a noise-assisted data analysis method, vol 193. Centre for Ocean-Land-Atmosphere Studies Technical Report, p 51

    Google Scholar 

  • Xiong D, Fu W, Wang K, Fang P, Chen T, Zou F (2021) A blended approach incorporating TVFEMD, PSR, NNCT-based multi-model fusion and hierarchy-based merged optimization algorithm for multi-step wind speed prediction. Energy Convers Manag 230:113680

    Google Scholar 

  • Yang Y, Guo H, Jin Y, Song A (2021) An ensemble prediction system based on artificial neural networks and deep learning methods for deterministic and probabilistic carbon price forecasting. Front Environ Sci 9:740093

    Google Scholar 

  • Yao Z, Xie J, Tian Y, Huang Q (2019) Using Hampel identifier to eliminate profile-isolated outliers in laser vision measurement. J Sens 2019:1–12

    Google Scholar 

  • Yi L, Li Z, Yang L, Liu J (2017) The scenario simulation analysis of the EU ETS carbon price trend and the enlightenment to China. J Environ Econ 2017:22–35

    Google Scholar 

  • Yun P, Huang X, Wu Y, Yang X (2022) Forecasting carbon dioxide emission price using a novel mode decomposition machine learning hybrid model of CEEMDAN-LSTM. Energy Science & Engineering

    Google Scholar 

  • Zhang F, Wen N (2022) Carbon price forecasting: a novel deep learning approach. Environ Sci Pollut Res 29:54782–54795

    Google Scholar 

  • Zhang, X., Chen, X., Yao, L., Ge, C. and Dong, M. (2019a) Deep neural network hyperparameter optimization with orthogonal array tuning. arXiv preprint arXiv:1907.13359

  • Zhang, X., Yao, L., Huang, C., Sheng, Q. Z. and Wang, X. (2017) Intent recognition in smart living through deep recurrent neural networks. arXiv preprint arXiv:1702.06830

  • Zhang Y, Liu K, Qin L, An X (2016) Deterministic and probabilistic interval prediction for short-term wind power generation based on variational mode decomposition and machine learning methods. Energy Convers Manag 112:208–219

    Google Scholar 

  • Zhang Z, Qin H, Liu Y, Yao L, Yu X, Lu J, Jiang Z, Feng Z (2019b) Wind speed forecasting based on quantile regression minimal gated memory network and kernel density estimation. Energy Convers Manag 196:1395–1409

    Google Scholar 

  • Zhao Y, Zhao H, Li B, Wu B, Guo S (2022) Point and interval forecasting for carbon trading price: a case of 8 carbon trading markets in China. Research Square

    Google Scholar 

  • Zhou F, Huang Z, Zhang C (2022) Carbon price forecasting based on CEEMDAN and LSTM. Appl Energy 311:118601

    Google Scholar 

  • Zhu B, Han D, Wang P, Wu Z, Zhang T, Wei Y-M (2017) Forecasting carbon price using empirical mode decomposition and evolutionary least squares support vector regression. Appl Energy 191:521–530

    Google Scholar 

  • Zhu B, Wei Y (2013) Carbon price forecasting with a novel hybrid ARIMA and least squares support vector machines methodology. Omega 41:517–524

    Google Scholar 

  • Zhu BZ, Ye SX, Wang P, He KJ, Zhang T, Wei YM (2018) A novel multiscale nonlinear ensemble leaning paradigm for carbon price forecasting. Energy Econ 70:143–157

    Google Scholar 

Download references

Acknowledgements

The authors express deep appreciation to the editors and reviewers for reading the manuscript tediously and for providing valuable suggestions and remarks.

Funding

This research was funded by the Project of Sichuan Oil and Natural Gas Development Research Center (Grant No. SKB20-06) and the Strategic Research and Consulting Project of the Chinese Academy of Engineering (2022-28-33, 2023-HZ-10).

Author information

Authors and Affiliations

  1. College of Management Science, Chengdu University of Technology, Chengdu, 610059, China

    Wang Yue, Wang Zhong, Wang Xiaoyi & Kang Xinyu

Authors
  1. Wang Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wang Xiaoyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kang Xinyu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Wang Yue wrote and revised the original manuscript. Wang Xiaoyi Wang performed data collection and treatment. Wang Zhong contributed to the conception of the study. Kang Xinyu reviewed and revised the manuscript. All authors commented on previous versions of the manuscript and read and approved the final manuscript.

Corresponding author

Correspondence to Wang Zhong.

Ethics declarations

Ethics approval

This study follows all ethical practices during writing.

Consent to participate

This is not applicable.

Consent for publication

This is not applicable.

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Responsible Editor: Ilhan Ozturk

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yue, ., Zhong, W., Xiaoyi, W. et al. Multi-step-ahead and interval carbon price forecasting using transformer-based hybrid model. Environ Sci Pollut Res 30, 95692–95719 (2023). https://doi.org/10.1007/s11356-023-29196-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11356-023-29196-z

Keywords

Search

Navigation