Interval price predictions for coal using a new multi-scale ensemble model

Accurate coal price prediction is important for the development of coal policy and prevention of coal market risks. The aim of this paper is to forecast coal prices in China by enhancing the performance of the variational mode decomposition (VMD) using an arithmetic optimization algorithm (AOA), which is then combined with N-BEATS, quantile regression (QR), and mean impact value algorithms (MIV) to create a new multi-scale ensemble forecasting model (VANQM). First, we use VMD that has been enhanced by the AOA to separate the coal price time series. Second, N-BEATS improved by QR is utilized to forecast the subsequences. The results of coal price interval forecasting are yielded. Finally, we use MIV to analyze how much variables affect coal prices. The findings of the study indicate that: the three key variables that have the greatest impact on coal prices are coal mining industry index, coal industry index, and A-share electricity industry index; the effect of the model's interval prediction is superior to the deterministic prediction in its current state; when the confidence levels are at 70 %, 80 %, and 90 %, PICP values of VANQM model are greater than the corresponding confidence levels. To summarize, when compared to the benchmark model, VANQM performs more accurately and consistently.