Data from: Predicting regional carbon price in China based on multi-factor HKELM by combining secondary decomposition and ensemble learning

Accurately predicting carbon price is crucial for risk avoidance in the
carbon financial market. In light of the complex characteristics of the
regional carbon price in China, this paper proposes a model to forecast
carbon price based on the multi-factor hybrid kernel-based extreme
learning machine (HKELM) by combining secondary decomposition and ensemble
learning. Variational mode decomposition (VMD) is first used to decompose
the carbon price into several modes, and range entropy is then used to
reconstruct these modes. The multi-factor HKELM optimized by the sparrow
search algorithm is used to forecast the reconstructed subsequences, where
the main external factors innovatively selected by maximum information
coefficient and historical time-series data on carbon prices are both
considered as input variables to the forecasting model. Following this,
the improved complete ensemble-based empirical mode decomposition with
adaptive noise and range entropy are respectively used to decompose and
reconstruct the residual term generated by VMD. Finally, the nonlinear
ensemble learning method is introduced to determine the predictions of
residual term and final carbon price. In the empirical analysis of
Guangzhou market, the root mean square error (RMSE), mean absolute error
(MAE) and mean absolute percentage error (MAPE) of the model are 0.1716,
0.1218 and 0.0026, respectively. The proposed model outperforms other
comparative models in predicting accuracy. The work here extends the
research on forecasting theory and methods of predicting the carbon price.