An ensemble dynamic self-learning model for multiscale carbon price forecasting

Precise carbon price forecasting can provide decision support for policy-makers and investors. However, due to the high non-stationarity and nonlinearity of carbon price series, it is difficult to get accurate forecasting results under volatile situations. To accommodate different scenarios, this paper proposes a dynamic self-learning integrating forecasting model to forecast the carbon price by considering external impact factors. The multi-dimensional time series is initially decomposed into different intrinsic mode functions simultaneously by the noise-assisted multivariate empirical mode decomposition method. After reconstructing the decomposed series into high-frequency, low-frequency, and trend modules, the extreme learning machine optimized by the cosine-based whale optimization algorithm is proposed to predict the carbon price. The dynamic relationships between the carbon price and impact factors are simulated by the sliding window structure, which improves the adaptability of the proposed model. The high prediction accuracy under different situations including extreme scenarios demonstrates the stability of the proposed model. A self-learning algorithm, which can automatically learn the evolving model structure and update model parameters, is designed to alleviate the underfitting/overfitting problem. The comparison results with existing models indicate the superiority of the proposed model.