Forecasting the carbon price of China's national carbon market: A novel dynamic interval-valued framework

To better describe the dynamic pattern of carbon price and enhance the forecasting accuracy, a novel dynamic interval forecasting framework is proposed in this paper designed to forecast the carbon price of the national carbon market launched in 2021 in China. In the first place, variables that may influence the volatility of carbon price are selected and analyzed to explore their relationship with the carbon price, where nonlinearity, dynamic and heterogeneity are found. Then, the original interval carbon price series is decomposed into several sub-sequences by Bivariate Empirical Mode Decomposition (BEMD). Subsequently, the sample entropy (SE) values are calculated to divide the sub-sequences into high-frequency ones and low-frequency ones. The selected energy, economic, environmental, and public attention variables function as predictive variables when forecasting the sub-sequences. The high-frequency sub-sequences are forecasted by a dynamic version of the extreme learning machine (dyELM) proposed in this paper that utilizes the volatility spillover index to embody the heterogenous predictive power among variables, where variables with larger volatility spillover are likely to be assigned with greater weights, while the low-frequency sub-sequences are forecasted by autoregressive conditional interval model with exogenous variables (ACIX). Finally, the forecasting results of sub-sequences are aggregated to obtain the forecasting result of the original interval carbon price series. Forecasting error evaluation and robustness check reveal that the proposed model outperforms the benchmark models, indicating the superiority and reliability of our model and the effectiveness of selected variables.