Given the complex characteristics of carbon price series,such as nonlinearity and non-smoothness,the prediction is quite challenging.Here,we propose TTBiGRUA as a carbon price prediction model that combines Time-Varying Filter Empirical Mode Decomposition (TVFEMD),Sample Entropy (SE),Bidirectional Gated Recurrent Unit (BiGRU) and Autoregressive Integrated Moving Average (ARIMA).First,the carbon price series were decomposed into mode components with different frequencies by TVFEMD;then,the sample entropy was used to evaluate the complexity of each component,and the K-means algorithm was applied for reconstruction.Subsequently,secondary TVFEMD was performed on the most volatile reconstructed mode components to further extract features and reduce modal aliasing.The components were separated into high-frequency and low-frequency categories according to the sample entropy values.The high-frequency components were predicted by BiGRU,while the low-frequency components were predicted by ARIMA,and the final prediction results were obtained by superimposing all component predictions.Using actual carbon price data from Guangdong and Hubei carbon markets in China,we evaluated the model's predictive validity and robustness through five evaluation indicators and the Diebold-Mariano (DM) test.Results show that the proposed model outperforms other benchmark comparison models in predictive accuracy.