Carbon price forecasting and pricing are critical for stabilizing carbon markets, mitigating investment risks, and fostering economic development. This paper presents an advanced decomposition-integration framework which seamlessly integrates econometric models with machine learning techniques to enhance carbon price forecasting. First, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method is employed to decompose carbon price data into distinct modal components, each defined by specific frequency characteristics. Then, Lempel–Ziv complexity and dispersion entropy algorithms are applied to analyze these components, facilitating the identification of their unique frequency attributes. The framework subsequently employs GARCH models for predicting high-frequency components and a gated recurrent unit (GRU) neural network optimized by the grey wolf algorithm for low-frequency components. Finally, the optimized GRU model is utilized to integrate these predictive outcomes nonlinearly, ensuring a comprehensive and precise forecast. Empirical evidence demonstrates that this framework not only accurately captures the diverse characteristics of different data components but also significantly outperforms traditional benchmark models in predictive accuracy. By optimizing the GRU model with the grey wolf optimizer (GWO) algorithm, the framework enhances both prediction stability and adaptability, while the nonlinear integration approach effectively mitigates error accumulation. This innovative framework offers a scientifically rigorous and efficient tool for carbon price forecasting, providing valuable insights for policymakers and market participants in carbon trading.