Forecasting Regional Carbon Prices in China Based on Secondary Decomposition and a Hybrid Kernel-Based Extreme Learning Machine

Accurately forecasting carbon prices is key to managing associated risks in the financial market for carbon. To this end, the traditional strategy does not adequately decompose carbon prices, and the kernel extreme learning machine (KELM) with a single kernel function struggles to adapt to the nonlinearity, nonstationarity, and multiple frequencies of regional carbon prices in China. This study constructs a model, called the VMD-ICEEMDAN-RE-SSA-HKELM model, to forecast regional carbon prices in China based on the idea of 'decomposition-reconstruction-integration'. The VMD is first used to decompose carbon prices and the ICEEMDAN is then used to decompose the residual term that contains complex information. To reduce the systematic error caused by increases in the mode components of carbon price, range entropy (RE) is used to reconstruct the results of its secondary decomposition. Following this, HKELM is optimized by the sparrow search algorithm and used to forecast each subseries of carbon prices. Finally, predictions of the price of carbon are obtained by linearly superimposing the results of the forecasts of each of its subseries. The results of experiments show that the secondary decomposition strategy proposed in this paper is superior to the traditional decomposition strategy, and the proposed model for forecasting carbon prices has significant advantages over a considered reference group of models.