Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 50 min ago
Peer-reviewedCC BY 4.0Mathematics

Interval Carbon Price Forecasting Based on Multi-Task Learning

  • Kaijie Chen1
  • Dinggao Liu2
  • Wen Han1
  • Zhenpeng Tang1
  • Yuqi Zheng1
  1. 1College of Economics and Management, Fujian Agriculture and Forestry University, Fuzhou 350002, China
  2. 2College of Forestry, Fujian Agriculture and Forestry University, Fuzhou 350002, China
Open at sourceDOICite

Abstract

Existing interval carbon price forecasting methods usually estimate the upper and lower bounds independently or derive them from point forecasts, overlooking their intrinsic coupling and risking logically inconsistent outputs. We propose a constrained multi-task learning framework, CMTL-ATCN, that treats interval-valued carbon prices as coupled tasks and optimizes them jointly under logical consistency constraints. The model uses attention-enhanced temporal convolutional networks (ATCN) to extract shared and task-specific features from multi-source data, which are then fused and decoded through dual task heads; all parameters are optimized jointly with a loss function that adds a logic penalty enforcing agreement between the two bounds. On China’s national (CEA), Guangdong (GDEA), and Hubei (HBEA) carbon markets, CMTL-ATCN attains the lowest interval forecast errors among deep models and eliminates logical inconsistencies entirely with zero violations. The results indicate that the proposed framework is promising for interval-valued forecasting in complex environments.

Related

  1. The price of multi-group transductive learning
    Noah Bergam, Samuel Deng, Daniel Hsu
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  2. TRACE: A Reproducible Benchmark for Electricity Price Forecasting with Official Operational Text
    Xinyi Yi, Zhangdie Yuan, Ioannis Lestas
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. PRICE: A Systematic Study of LLM Adaptation Choices for Bitcoin Price Forecasting
    Maryam Fakhari, Mehran Safayani
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Leveraging Continuous Trade Data for Intraday Imbalance Price Forecasting
    Klimis Stylpnopoulos, Jethro Browell, Janine Illian +2
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  5. Day-Ahead Electricity Price Forecasting Using a Multivariate Group Lasso Method
    Keyi Wang, Jiaxiang Ji, Mahan Mansouri +1
    arXivPreprintCC BY-NC-ND 4.0Full textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@article{chen2026interval,
  title = {{Interval Carbon Price Forecasting Based on Multi-Task Learning}},
  author = {Kaijie Chen and Dinggao Liu and Wen Han and Zhenpeng Tang and Yuqi Zheng},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203672},
  url = {https://www.mdpi.com/2227-7390/14/20/3672},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Interval Carbon Price Forecasting Based on Multi-Task Learning
AU  - Kaijie Chen
AU  - Dinggao Liu
AU  - Wen Han
AU  - Zhenpeng Tang
AU  - Yuqi Zheng
PY  - 2026
DA  - 2026/10/10
JO  - Mathematics
DO  - 10.3390/math14203672
UR  - https://www.mdpi.com/2227-7390/14/20/3672
AB  - Existing interval carbon price forecasting methods usually estimate the upper and lower bounds independently or derive them from point forecasts, overlooking their intrinsic coupling and risking logically inconsistent outputs. We propose a constrained multi-task learning framework, CMTL-ATCN, that treats interval-valued carbon prices as coupled tasks and optimizes them jointly under logical consistency constraints. The model uses attention-enhanced temporal convolutional networks (ATCN) to extract shared and task-specific features from multi-source data, which are then fused and decoded through dual task heads; all parameters are optimized jointly with a loss function that adds a logic penalty enforcing agreement between the two bounds. On China’s national (CEA), Guangdong (GDEA), and Hubei (HBEA) carbon markets, CMTL-ATCN attains the lowest interval forecast errors among deep models and eliminates logical inconsistencies entirely with zero violations. The results indicate that the proposed framework is promising for interval-valued forecasting in complex environments.
SN  - 2227-7390
ER  -