In the context of international carbon neutrality, energy prices are affected by several nonlinear and nonstationary factors, making it challenging for traditional forecasting models to predict energy prices effectively. The existing literature mainly uses linear models or a combination of multiple models to forecast energy prices. For the nonlinear relationship between variables and the mining of historical data information, the prediction strategy and accuracy of the existing literature need to be improved. Thus, this paper improves the prediction accuracy of energy prices by developing a “decomposition-reconstruction-integration” thinking strategy that affords medium- and short-term energy price prediction based on carbon constraint, eigenvalue transformation and deep learning neural networks. Considering 2011–2020 as the research period, the prices for traditional energy resources and polysilicon in clean photovoltaic energy raw materials are selected as representatives. Based on energy price decomposition using the Singular Spectrum Analysis (SSA) method, and combining it with Learning Vector Quantization (LVQ) cluster technology, the decomposed quantities are aggregated into price sequences with different characteristics. Additionally, the carbon intensity is considered the leading market’s overall constraint, which is input with the processed price data into a Long Short-Term Memory network (LSTM) model for training. Thus, the SSA-LSTM combined forecasting model is developed to predict the energy price under carbon neutrality. Four indices are employed to evaluate the prediction accuracy: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and R-squared. The results highlight the following observations. (1) Using a sequence decomposition clustering strategy significantly improves the model’s prediction accuracy. This strategy enhances predicting the overall trend of the price series and the changes in different periods. For coal price, the RMSE value decreased from 0.135 to 0.098, the MAE value decreased from 0.087 to 0.054, the MAPE value decreased from 0.072 to 0.064, and the R-squared value increased from 0.643 to 0.725. Regarding the polysilicon price, the RMSE value decreased from 0.121 to 0.096, the MAE value decreased from 0.068 to 0.064, the MAPE value decreased from 0.069 to 0.048, and the R-squared value increased from 0.718 to 0.764. (2) The prediction effect is better in the case of carbon constraint. Considering “carbon emission intensity” as the overall constraint of the leading market, it can effectively explore the typical characteristics of energy price information. Four evaluation indicators show that the accuracy of the model prediction can be improved by more than 3%. (3) When the proposed SSA-LSTM model is used to predict both prices, the results show that the evaluation index of the prediction error remained at about 1%, while the model’s accuracy was high. This also proves that the proposed model can predict traditional energy prices and new energy sources such as solar energy.
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