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

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.