A novel multiscale nonlinear ensemble leaning paradigm for carbon price forecasting

In this study, a novel multiscale nonlinear ensemble leaning paradigm incorporating empirical mode decomposition (EMD) and least square support vector machine (LSSVM) with kernel function prototype is proposed for carbon price forecasting. The EMD algorithm is used to decompose the carbon price into simple intrinsic mode functions (IMFs) and one residue, which are identified as the components of high frequency, low frequency and trend by using the Lempel-Ziv complexity algorithm. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is used to forecast the high frequency IMFs with ARCH effects. The LSSVM model with kernel function prototype is employed to forecast the high frequency IMFs without ARCH effects, the low frequency and trend components. The forecasting values of all the components are aggregated into the ones of original carbon price by the LSSVM with kernel function prototype-based nonlinear ensemble approach. Furthermore, particle swarm optimization is used for model selections of the LSSVM with kernel function prototype. Taking the popular prediction methods as benchmarks, the empirical analysis demonstrates that the proposed model can achieve higher level and directional predictions and higher robustness. The findings show that the proposed model seems an advanced approach for predicting the high nonstationary, nonlinear and irregular carbon price