MLP-Carbon: A new paradigm integrating multi-frequency and multi-scale techniques for accurate carbon price forecasting

Accurate carbon price forecasting is crucial for market participants, as it facilitates decision-making based on comprehensive information, thereby ensuring effective management and stable operation of the carbon market. However, due to the influence of various factors on carbon price data, exhibiting high levels of randomness and volatility, traditional point prediction models often fail to provide decision-makers with sufficient and effective information. To this end, this paper proposes a novel carbon price forecasting paradigm: MLP-Carbon. Utilizing two learning frameworks, MLP-Carbon-Point Forecasting (MLP-Carbon-PF in short) and MLP-Carbon-Interval Forecasting (MLP-Carbon-IF in short), the proposed paradigm delivers accuracy point forecasting results and high-quality probabilistic forecasting intervals, thereby enriching the provided information. Specifically, we first denoise the original carbon price data adopting Variational Mode Decomposition (VMD), and then extract multi-frequency and multi-scale information from the data using the multi-scale sample entropy (MSSE) based secondary decomposition–recombination method and fuzzy information granulation (FIG) respectively. Additionally, interpretable feature engineering techniques are utilized to select beneficial features to assist training. After the above multi-stage data processing, we propose two deep learning frameworks based on fully multi-layer perceptrons (MLP), which can fit and learn relevant information through parallel multi-frequency learning block and multi-scale learning block, and finally summarize the learned information and output the forecasting result. MLP-Carbon-IF achieves the simultaneous output of the forecasting interval’s upper and lower bounds through the parameter-sharing technique and a customized loss function based on Quantile Regression (QR), which focuses on the deviation of the actual values relative to the center of the interval. Experiments using real data from two carbon markets in Guangdong and Hubei demonstrate that MLP-Carbon significantly outperforms the benchmarks. Through ablation experiments, the unique contribution of each block in the learning framework is also verified.