| In recent years,the global carbon emissions trading system has shown a trend of expansion,and diversified carbon markets have been established around the world as an important policy tool for carbon neutrality.As the largest developing country in the world,China consciously assumes the responsibility for emission reduction and actively promotes carbon emission trading.With the official launch of the national unified carbon market in Shanghai Environment and Energy Exchange,the trading volume of China’s carbon market will surpass the EU ETS and become the largest carbon trading market in the world.Its development will be full of opportunities and challenges.Accurate carbon price prediction is a requirement for the stable operation of the carbon market,and it is also an important guarantee for further playing the role of carbon price signals in guiding investment,managing risks,and stabilizing market expectations.In view of the chaotic and non-stationary characteristics of carbon prices,this paper establishes a combined forecasting framework for carbon emission rights prices that combines data processing,optimization improvement and forecasting research.First,the original carbon price sequence was analyzed by variational mode decomposition(VMD),and the intrinsic correlation of each modal component was obtained by partial autocorrelation analysis.By introducing the adversarial learning strategy and the sinecosine algorithm to improve the butterfly optimization algorithm,a hybrid improved butterfly optimization algorithm(EBOA)is proposed,and the EBOA is used to realize the optimization of the input layer weights and the hidden layer thresholds of the extreme learning machine(ELM).On this basis,a forecasting portfolio optimization model of VMD-EBOA-ELM is constructed to establish a basis for accurate carbon price forecasting.The representative actual data of Guangdong carbon market and Hubei carbon market are selected for empirical analysis.The results show that the model proposed in this paper has excellent robustness and excellent forecasting performance,and could achieve highprecision carbon price point forecasting.Meanwhile,in view of the uncertainty of carbon price series fluctuations,the non-parametric kernel density estimation is adopted for the error of the point prediction results,and the interval prediction of carbon prices under different confidence levels is successfully realized.The experimental results show that the carbon price prediction interval of the VMD-EBOA-ELM model has both stability and reliability.With the continuous enhancement of the financial attributes of the carbon market,carbon price signals play an increasingly important role in maintaining market stability and guiding the low-carbon transition of society.Accurate carbon price forecasts have important theoretical and practical implications for carbon market construction.significance.Therefore,starting from the carbon price data itself,this paper establishes a high-precision carbon price prediction composite model.In addition,the probability interval prediction is introduced into the field of carbon price prediction to describe the randomness of carbon price fluctuations,in order to provide valuable reference information for the risk management of the carbon market. |