Nexus Among Innovation, Energy, Economic Structure, and CO2 Emissions in China: Evidence from a Bayesian Fourier ARDL Approach

China’s carbon mitigation challenge is intricately linked to energy consumption, income growth, innovation performance, and sectoral structure. Using annual aggregate data for 1995–2021, this study investigates these dynamics using Fourier ARDL and Bayesian Fourier ARDL specifications, while evaluating sectoral shares through predictive-content tests. Crucially, the empirical evidence demonstrates that emissions are not cointegrated with the explanatory series. Unresolved integration-order diagnostics formally preclude bounds-test interpretation, establishing that the model yields no verified equilibrium relationship. In first differences, energy consumption displays a strong contemporaneous short-run association with emissions. While the implied lagged-level coefficient ratio for energy is near unity, it captures dynamic parameter scaling within the short-sample ARDL specification. The implied ratios for GDP and aggregate innovation are small, statistically insignificant, and encompass zero. Evidence for an Environmental Kuznets Curve (EKC) is highly specification-dependent, and Granger-causality tests reveal frequency-sensitive short-run predictive content in differenced data, without evidence of permanent structural links. In the absence of automatic error correction, mitigation policy cannot rely on assumed steady-state adjustments, underscoring the necessity of direct, structural decarbonization of the energy mix. The findings demonstrate that long-term environmental sustainability cannot be achieved through passive economic maturation, requiring deliberate structural reforms to align industrial growth with carbon neutrality commitments.