Multi-step-ahead and interval carbon price forecasting using transformer-based hybrid model

Abstract

Accurate and stable carbon price forecasts provide a reference for the stability of the carbon market and significantly improve investment and operational decisions. However, due to the non-linear and non-stationarity characteristics of carbon price series and its complex fluctuation features, realizing this goal is still a significant challenge, and researchers usually ignore multi-step and interval forecasting. To accurately predict the carbon price, a novel hybrid multi-step and interval carbon price forecasting model is proposed in this study, based on Hampel identifier(HI), time-varying filtering-based empirical mode decomposition (TVFEMD), and Transformer. Firstly, HI identifies and corrects outliers in carbon price. Then, carbon price is decomposed by TVFEMD into several intrinsic mode functions(imfs) to reduce the non-linear and non-stationarity of carbon price, to obtain more regular features in series, and these imfs are reconstructed by sample entropy(SE). Subsequently, the Orthogonal Array Tuning Method(OATM) is used to optimize the Transformer's hyperparameters to obtain the optimal model structure. Finally, The Transformer after hyperparameter optimization and quantile loss function is used to perform multi-step and interval forecasting on each part of the reconstruction, and the final prediction result is obtained by summing them up. Five pilot carbon trading markets in China were selected as experimental objects to verify the proposed model's prediction performance, and a variety of benchmark models and evaluation indicators were selected for comparison and analysis. The experimental results show that the proposed hybrid model is superior to the benchmark model in most aspects, and the interval forecast can well describe the uncertainty of carbon price fluctuations. Therefore, the proposed hybrid model is a reliable carbon price forecasting tool that can provide a reliable reference for policymakers and investors.