Forecasting interval carbon price through a multi-scale interval-valued decomposition ensemble approach

This paper proposes a novel Multi-scale Interval-valued Decomposition Ensemble (MIDE) framework for forecasting European Union Allowance (EUA) carbon futures prices, which integrates Noise-assisted Multivariate Empirical Mode Decomposition (NAMEMD), Interval-valued Vector Auto-Regressive (IVAR) model, Interval Event Analysis (IEA) method, and Interval Multi-Layer Perceptron (IMLP). First, the original interval-valued carbon prices with other interval-valued control variables are decomposed and integrated into high, medium, and low-frequency components by NAMEMD. Second, IVAR is used to investigate the dynamics of the interval-valued vector system in low-frequency components, while IMLP is employed to characterize the high-frequency components. Besides, the interval event analysis investigates typical events that significantly impact carbon prices in the medium-frequency component. Furthermore, empirical findings indicate that our proposed MIDE learning approach significantly outperforms some other benchmark models in out-of-sample forecasting.