Estimating China’s CO(2) emissions under the influence of COVID-19 epidemic using a novel fractional multivariate nonlinear grey model

The COVID-19 pandemic has posed a severe challenge to the global economic recovery and China’s economic growth. Although China has achieved stage victory against the epidemic, the impact and influence of the epidemic on China’s economy will linger. On the positive side, the epidemic has led to a dramatic reduction in air pollution levels and a sharp slowdown in greenhouse gas emissions such as CO(2). Forecasting China’s CO(2) emissions under the impact of the COVID-19 epidemic is crucial for formulating policies that contribute to smooth economic development and rational energy consumption. To this end, this paper improves on the traditional grey model, GM(1, N), by developing a novel fractional multivariate nonlinear grey model, FMNGM(q, N). These improvements include two key points. First, different power exponents are assigned to each relevant factor variable to explain their nonlinear, uncertain, and complicated relationships with the system characteristic variables. Second, the integer accumulation is changed to fractional accumulation to preprocess the data, and the Caputo-type fractional derivative is used to characterize the endogenous relationships among the system characteristic data. In addition, the quantum particle swarm optimization (QPSO) algorithm is used to optimize the above parameters with the goal of minimizing MAPE. The collected data on China’s CO(2) emission from 2001 to 2018 were divided into two parts according to different stages of economic development: 2001–2009 and 2010–2018. Both sets of data were modelled and analysed separately and compared with other models. Results showed that the proposed model had better prediction accuracy than other models. Finally, the model built using the 2010–2018 data was used to forecast China’s CO(2) emissions. Results show that China’s CO(2) emissions in 2020 under the impact of COVID-19 will decrease by approximately 3.15% from 2019 to 9893 million tons. The results bear important policy implications for planners in investment in clean energy and infrastructure to achieving the goal of a low-carbon transition.