A multiscale and multivariable differentiated learning for carbon price forecasting

Carbon price forecasting is important for policymakers and market participants. Due to the non-stationary and non-linearity of the carbon price, the commonly used methods adopt the ideology of 'decomposition and integration' to conduct multiscale forecasting. On this basis, multivariable forecasting discovers more informative knowledge with exogenous variables for carbon price forecasting, but it ignores that (i) the high-frequency and low-frequency components of the carbon price are mainly affected by different variables, and (ii) each variable contributes differently to each component forecasting. To address these challenges, we propose a multiscale and multivariable differentiated learning method for carbon price forecasting in this study. Specifically, different variables are introduced to forecast the high-frequency and low-frequency components, and a novel attention-weighted least squares support vector regression method is first proposed, in which the weight matrix of variables is constructed according to the idea of the attention mechanism. Furthermore, we analyze the contribution of each variable to the carbon price using Shapley additive explanations, thereby providing a reference for carbon market participants. We conduct experiments on the carbon price of the European Union Emissions Trading System and Hubei carbon market in China. Extensive results demonstrate that the proposed model achieves competitive and superior performance over the baseline and compared models.