Accurate carbon price forecasts are crucial for policymakers and enterprises to understand the dynamics of carbon price fluctuations, enabling them to formulate informed policies and investment strategies. However, due to the non-linear and non-stationary nature of carbon price, traditional models often struggle to achieve high prediction accuracy. To address this challenge, this study proposes a novel integrated prediction framework designed to enhance forecast accuracy. First, the carbon price series is decomposed into a series of smoother subsequences using fast iterative filtering (FIF). Subsequently, an integrated prediction model, AM-TCN-LSTM, is constructed, incorporating the attention mechanism (AM), temporal convolutional networks (TCN), and long short-term memory (LSTM) neural networks. The attention mechanism adaptively captures complex features from multiple factors, while the TCN-LSTM efficiently extracts temporal features from the sequences. Finally, the results from each subsequence are aggregated to generate the final prediction. Five carbon markets in china: Guangdong, Hubei, Shenzhen, Beijing, and Shanghai were selected to verify the validity of the proposed model. Various comparative models and evaluation metrics were employed to assess performance. The results demonstrate that: (1) the TCN-LSTM model achieves higher prediction accuracy compared to single models. (2) FIF is a more effective decomposition method with superior performance compared to EMD-based methods. (3) The proposed model exhibits the highest predictive capability, with MAE values of 0.0964, 0.1403, 1.9476, 2.0848, and 0.5029 for the five carbon markets, significantly outperforming comparison models. (4) The attention mechanism effectively captures the influence of multiple factors on carbon price, particularly within the short-term components.