Carbon emission price point-interval forecasting based on multivariate variational mode decomposition and attention-LSTM model

Accurate forecasting of carbon emission prices is a crucial yet challenging task, given the complexity of the trading market and the variability of influencing factors. To comprehensively address factors related to carbon prices while considering interval forecasts associated with uncertainty, this study introduces a novel multistep ahead point-interval forecasting framework for carbon emission prices. This framework integrates multifactor selection, multivariate decomposition and reconstruction, an intelligent point and interval forecasting network, and an evaluation system. First, influencing factors are selected using a recursive feature elimination algorithm based on the extreme gradient boosting estimator. Second, original carbon prices and related influencing factors are decomposed into a set of multimode components (MMCs) using multivariate variational mode decomposition and sample entropy reconstruction techniques. Third, each row of MMCs is predicted using a long short-term memory model with an attention mechanism, and final point predictions are produced through simple addition. Finally, interval predictions are derived using enhanced kernel density estimation (KDE), which can expand the upper and lower bounds of the prediction interval. The stability and robustness have been tested in European Union Allowance (EUA) price forecasting. The results show that the proposed model is superior to other benchmark models, with MAPEs of 0.83%, 3.54%, and 3.82% in 1-step, 15-step, and 30-step ahead forecasting, respectively. Additionally, the proposed enhanced KDE demonstrates excellent performance; in 1-step ahead forecasting, the F-value is 1.86, 1.82, and 1.75 at the 80%, 90%, and 95% confidence levels, respectively. This proves that the proposed framework can effectively improve the point forecasting performance of EUA prices and quantify the prediction uncertainty.