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Accurately predicting carbon trading prices using deep learning models can help enterprises understand the operational mechanisms and regulations of the carbon market. This is crucial for expanding the industries covered by the carbon market and ensuring its stable and healthy development. To ensure the accuracy and reliability of the predictions in practical applications, it is important to evaluate the model's robustness. In this paper, we built models with different parameters to predict carbon trading prices, and proposed models with high accuracy and robustness. The accuracy of the models was assessed using traditional survey indicators. The robustness of the CNN-LSTM model was compared to that of the LSTM model using Z-scores. The CNN-LSTM model with the best prediction performance was compared to a single LSTM model, resulting in a 9% reduction in MSE and a 0.0133 shortening of the Z-score range. Furthermore, the CNN-LSTM model achieved a level of accuracy comparable to other popular models such as CEEMDAN, Boosting, and GRU. It also demonstrated a training speed improvement of at least 40% compared to the aforementioned methods. These results suggest that the CNN-LSTM enhances model resilience. Moreover, the practicality of using Z-score to evaluate model robustness is confirmed. • Deep learning by combined CNN-LSTM networks for carbon price forecasting. • Hyperparameter tuning of deep learning models for improving forecast accuracy. • CNN-LSTM models outperform single CNN models and single LSTM models. • Performance metric of deep learning for abrupt changes in carbon price variation. [ABSTRACT FROM AUTHOR]

This paper analyzes the overall and time-varying efficiency of China's carbon market, which is crucial for carbon risk management and policymaking. Due to the severe illiquidity problems other pilots face, we first select Shenzhen, Guangdong, and Hubei pilots out of the eight carbon pilots for our study based on the statistical analysis. We then test the overall efficiency of the markets using the LM, CD, and Wild-Bootstrap variance ratio test. The sliding window method is combined with the above three variance ratio test methods to validate the time-varying efficiency. The results prove that the overall efficiency of the three carbon pilots has not yet reached a weak form. And we observe that the short-term efficiency is time-varying and may be weak-form. The study further found Hubei to be the most efficient carbon pilot, followed by Guangdong and Shenzhen. Finally, this paper conducts a qualitative analysis on the low efficiency from five aspects namely carbon trading rules, market liquidity, price volatility, trading volume, and types of trading products. Several conclusions and recommendations are proposed for policymakers and investors. • Sliding window method is combined with a series of variance ratio test methods. • The overall and time-varying efficiency of China's carbon market is tested. • China's carbon market has not reached weak-form efficiency. • Hubei is the most efficient carbon pilot. • Reasons for low efficiency are analyzed. [ABSTRACT FROM AUTHOR]