This study aims to investigate the price changes in the carbon trading market and the development of international carbon credits in-depth. To achieve this goal, operational principles of the international carbon credit financing mechanism are considered, and time series models were employed to forecast carbon trading prices. Specifically, an ARIMA(1,1,1)-GARCH(1,1) model, which combines the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and Autoregressive Integrated Moving Average (ARIMA) models, is established. Additionally, a multivariate dynamic regression Autoregressive Integrated Moving Average with Exogenous Inputs (ARIMAX) model is utilized. In tandem with the modeling, a data index system is developed, encompassing various factors that influence carbon market trading prices. The random forest algorithm is then applied for feature selection, effectively identifying features with high scores and eliminating low-score features. The research findings reveal that the ARIMAX Least Absolute Shrinkage and Selection Operator (LASSO) model exhibits high forecasting accuracy for time series data. The model's Mean Squared Error, Root Mean Squared Error, and Mean Absolute Error are reported as 0.022, 0.1344, and 0.1543, respectively, approaching zero and surpassing other evaluation models in predictive accuracy. The goodness of fit for the national carbon market price forecasting model is calculated as 0.9567, indicating that the selected features strongly explain the trading prices of the carbon emission rights market. This study introduces innovation by conducting a comprehensive analysis of multi-dimensional data and leveraging the random forest model to explore non-linear relationships among data. This approach offers a novel solution for investigating the complex relationship between the carbon market and the carbon credit financing mechanism.