Predictive Recurrent Neural Networks Based Carbon Price Forecasting: A Generative Perspective

A novel predictive recurrent neural network (PRNN) framework is introduced for carbon price forecasting, which differs from previous approaches by making one-step ahead predictions over the entire carbon price sequence, rather than solely predicting the final time step. Leveraging autoregressive recurrent neural networks (RNNs), it is proved that minimizing the mean squared error (MSE) or mean absolute error (MAE) across all predictions is equivalent to the generative optimization objective of maximizing the likelihood of the complete carbon price sequence under Gaussian or Laplace assumption. This generative optimization objective facilitates the PRNN in capturing the stable temporal relationships within the complete carbon price sequence, thereby enhancing the accuracy of carbon price forecasting. Computational experiments are conducted on three publicly accessible carbon price datasets to evaluate the performance of the proposed PRNN in comparison to other well-established benchmarking models. Experimental results demonstrate that the proposed PRNN achieves superior forecasting performance, evidenced by lower average RMSE, MAE, MAPE, and higher average $${\text{R}}^{2}$$ R 2 . Additionally, it maintains significantly lower error variance across various evaluation metrics when compared to traditional RNNs. Results verify the advantage of applying the proposed PRNN for carbon price forecasting from the generative perspective.