Forecasting China’s CO \(_2\) emissions is critical to achieving the targets of carbon peaking and carbon neutrality. Given the insufficient information and nonlinear characteristics often associated with annual CO \(_2\) emission series, we propose a new unbiased fractional nonlinear grey Bernoulli model with a unified fractional grey generating operator (FGO-UFNGBM(1,1)). Specifically, we extend the value of fractional order generating operator to the real number domain for the fractional nonlinear grey Bernoulli model (FNGBM(1,1)). Furthermore, a new unbiased estimator is derived to eliminate the inherent bias associated with linear parameters. The model is subsequently solved using the particle swarm optimization (PSO) algorithm. Empirical results indicate that the proposed model outperforms various competing grey and non-grey models. Robustness tests conducted using probability density analysis and perturbation analysis, confirm that the proposed model provides reliable and robust predictions. Finally, the proposed model is applied to estimate China’s CO \(_2\) emissions for the next seven years. The forecasts suggest that China will face significant challenges in achieving the carbon peak target, more aggressive decarbonization policies need to be introduced to ensure win the dual-carbon goal.
