Accurate prediction of carbon trading prices is crucial for guiding investors to make informed decisions and assisting governments in formulating scientific carbon trading policies. This paper introduces a multisource data-driven carbon price composite forecasting model, aimed at enhancing prediction accuracy through advanced data processing and analysis methods. The model initially employs a secondary decomposition strategy, including Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Variational Mode Decomposition (VMD) methods, to decompose the original data series into three sub-sequences of different frequencies. Subsequently, it utilizes the Partial Autocorrelation Function (PACF) and Random Forest algorithm for feature selection to determine the input variables for different frequency sequences and conducts in-depth analysis and selection of influencing factors, including unstructured data. Furthermore, the model employs a multiscale forecasting strategy, combining Particle Swarm Optimization (PSO) enhanced Bidirectional Long Short-Term Memory (BiLSTM) and Extreme Gradient Boosting (XGBoost) models, along with the Autoregressive Integrated Moving Average (ARIMA) method, to predict based on the characteristics of different frequency components. Finally, the forecasts are integrated using PSO-BiLSTM to form a comprehensive forecast. Notably, given the high correlation between the trend series and influencing factor variables, the model jointly predicts them. A case study based on the Guangdong carbon market in China demonstrates that the proposed composite forecasting model outperforms other benchmark models, with Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) values of 0.4009, 0.2699, and 0.5183%, respectively. This forecasting model provides an effective tool for predicting and analyzing carbon price fluctuations, offering new insights for precise carbon market price predictions.