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Peer-reviewedCC BY 4.0Fractal and Fractional

Multiscale Nonlinear Risk Transmission in the Carbon–Fossil Energy–Clean Energy System from a Fractal-Market Perspective: Evidence from EMD–TVP-VAR and Interpretable Machine Learning

  • Shanshan Zheng1
  • Xiaoxu Du2
  • Min Tang2
  • Xiaowen Zhuang3
  • Gan Wang4
4 affiliations
  1. 1School of International Economics and Trade, Fujian Business University, Fuzhou 350012, China
  2. 2College of Finance, Fujian Jiangxia University, Fuzhou 350108, China
  3. 3College of Architecture and Urban Planning, Tongji University, Shanghai 200092, China
  4. 4University of Edinburgh Business School, University of Edinburgh, Edinburgh EH8 9JS, UK
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Abstract

Financial markets are complex systems characterized by heterogeneous trading horizons, nonlinear interactions, and scale-dependent dependence. From a fractal-market perspective, these features imply that risk transmission may vary across temporal scales and market states. This study examines multiscale connectedness among carbon, West Texas Intermediate (WTI) crude oil, coal, natural gas, and clean energy markets. Empirical mode decomposition (EMD) adaptively extracts intrinsic high- and low-frequency components, while time-varying parameter vector autoregression (TVP-VAR) is used to estimate connectedness across scales. Random forest, gradient boosting decision tree, extreme gradient boosting, and SHapley Additive exPlanations are employed to identify nonlinear and state-dependent macro-financial drivers. Results show pronounced scale heterogeneity: original connectedness closely tracks high-frequency dynamics, whereas low-frequency connectedness is stronger and more persistent, peaking during the 2022 energy crisis. Market roles are horizon-dependent, with WTI generally transmitting risk, carbon mainly receiving risk, and clean energy becoming an important low-frequency transmitter. Overall, the findings support a multiscale interpretation of carbon–energy risk transmission consistent with the heterogeneous-horizon view of fractal-market research.

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Cite

BibTeXRIS
BibTeX
@article{zheng2026multiscale,
  title = {{Multiscale Nonlinear Risk Transmission in the Carbon–Fossil Energy–Clean Energy System from a Fractal-Market Perspective: Evidence from EMD–TVP-VAR and Interpretable Machine Learning}},
  author = {Shanshan Zheng and Xiaoxu Du and Min Tang and Xiaowen Zhuang and Gan Wang},
  journal = {Fractal and Fractional},
  year = {2026},
  month = oct,
  doi = {10.3390/fractalfract10100711},
  url = {https://www.mdpi.com/2504-3110/10/10/711},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Multiscale Nonlinear Risk Transmission in the Carbon–Fossil Energy–Clean Energy System from a Fractal-Market Perspective: Evidence from EMD–TVP-VAR and Interpretable Machine Learning
AU  - Shanshan Zheng
AU  - Xiaoxu Du
AU  - Min Tang
AU  - Xiaowen Zhuang
AU  - Gan Wang
PY  - 2026
DA  - 2026/10/09
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10100711
UR  - https://www.mdpi.com/2504-3110/10/10/711
AB  - Financial markets are complex systems characterized by heterogeneous trading horizons, nonlinear interactions, and scale-dependent dependence. From a fractal-market perspective, these features imply that risk transmission may vary across temporal scales and market states. This study examines multiscale connectedness among carbon, West Texas Intermediate (WTI) crude oil, coal, natural gas, and clean energy markets. Empirical mode decomposition (EMD) adaptively extracts intrinsic high- and low-frequency components, while time-varying parameter vector autoregression (TVP-VAR) is used to estimate connectedness across scales. Random forest, gradient boosting decision tree, extreme gradient boosting, and SHapley Additive exPlanations are employed to identify nonlinear and state-dependent macro-financial drivers. Results show pronounced scale heterogeneity: original connectedness closely tracks high-frequency dynamics, whereas low-frequency connectedness is stronger and more persistent, peaking during the 2022 energy crisis. Market roles are horizon-dependent, with WTI generally transmitting risk, carbon mainly receiving risk, and clean energy becoming an important low-frequency transmitter. Overall, the findings support a multiscale interpretation of carbon–energy risk transmission consistent with the heterogeneous-horizon view of fractal-market research.
SN  - 2504-3110
ER  -