A carbon price ensemble prediction model based on secondary decomposition strategies and bidirectional long short‐term memory neural network by an improved particle swarm optimization

Abstract To further enhance the precision of carbon trading price forecasting, this research proposes a combined forecasting model, CEEMDAN–VMD–IPSO–BiLSTM, considering the unsatisfactory high‐frequency sequence decomposition and the reliance on unidirectional neural networks in current carbon price‐prediction models. First of all, the original sequence of carbon prices is decomposed into multiple independent subsequences through the completely ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique. The sample entropy values of each subsequence are calculated to reconstruct them as high‐frequency, low‐frequency, and trend sequences. Second, we employ the variational mode decomposition (VMD) approach to decompose the high‐frequency series. The obtained subsequences, along with the low‐frequency and trend sequences, are separately input into an improved particle swarm optimization (IPSO) optimized bidirectional long short‐term memory neural network (BiLSTM) model for forecasting. Finally, an IPSO–BiLSTM model is used to integrate the forecasting outcomes from the previous step, yielding the ultimate results for predicting carbon prices. The case studies reveal that compared with the benchmark model, this model exhibits superior predictive precision and universality. It offers theoretical support for optimizing carbon market operations and fostering low‐carbon economic growth, holding practical importance.