The emission peak and carbon neutrality targets pose a great challenge to carbon emission reduction in the coal industry, and the coal industry will face an all-around deep adjustment. The forecast of coal price is crucial for reducing carbon emissions in the coal industry in an orderly manner under the premise of ensuring national energy security. The volatility and instability of coal prices are a result of multiple influencing factors, making it very difficult to make accurate predictions of coal price changes. We propose in this paper an innovative hybrid forecasting method (CEEMDAN-GWO-CatBoost) for forecasting coal price indexes by combining machine learning models, feature selections, data decomposition, and model interpretation. By combining high forecasting accuracy with good interpretability, this method fills a gap in the field of coal price forecasting. Initially, we examine the factors that influence coal prices from five angles: Supply, demand, macroeconomic factors, freight costs, and substitutes; and we employ Spearman correlation analysis to reduce the complexity of the attribute set and devise a coal price forecasting index system. Secondly, the CEEMDAN method is used to decompose the raw coal price index data into seven intrinsic modal functions and one residual term in order to weaken the volatility of the data caused by complex factors. Next, the CatBoost model hyperparameters are optimized using the Grey Wolf Optimizer algorithm, while the coal price data is fed into the combined forecasting model. Lastly, the SHAP interpretation method is introduced for studying the important indicators affecting coal prices. The experimental results show that the combined CEEMDAN-GWO-CatBoost forecasting model proposed in this paper has significantly better forecasting performance than other comparative models, and the SHAP method employed in this study identifies the macroeconomic environment, freight costs, and coal import volume as significant factors affecting coal prices. As part of the contribution of this paper, specific recommendations are made to the government regarding the formulation of a regulatory policy for the coal industry in the context of carbon neutrality based on the findings of this research.