Probability density prediction for carbon allowance prices based on TS2Vec and distribution Transformer

Carbon allowance price is an important tool to reduce carbon emissions and achieve carbon neutrality. It is necessary to establish a predictive model to provide accurate and reliable information to managers and participants in the carbon trading market. Therefore, a novel probability density prediction model, called TS2Vec-based distribution Transformer (TDT), is proposed. TDT consists of two stages: contrastive unsupervised pre-training and supervised training. In the contrastive unsupervised training stage, time series to vector (TS2Vec) is used to represent the dynamic trends and unique features of the data. Then, these representations are fed into the distribution Transformer (DT) to fit the hypothetical probability distribution. Experimental results show that the prediction results of the proposed TDT are more accurate and reliable than other benchmark models. In addition, our research indicates reliable probability density predictions provide enterprises with opportunities to control carbon emission costs and increase economic returns, thereby improving the competitiveness of enterprises and promoting carbon emission reduction.