A combination forecasting model based on hybrid interval multi-scale decomposition: Application to interval-valued carbon price forecasting

Forecasting carbon price accurately is of great significance to ensure the healthy development of the carbon market. However, due to the non-linearity, non-stationarity, and dynamic uncertainty of interval-valued carbon price, there are many challenges to forecast the interval-valued carbon price precisely and stably. Therefore, this paper proposes a combination forecasting model based on the hybrid interval multi-scale decomposition method and its application to forecasting interval-valued carbon prices. First, three interval multi-scale decomposition methods, including interval discrete wavelet transform method (IDWT), interval empirical mode decomposition method (IEMD), and interval variational mode decomposition method (IVMD), are developed to decompose the interval-valued carbon price into interval trend and residuals. Second, Generalized autoregressive conditional heteroskedasticity (GARCH), auto-regressive integrated moving average model (ARIMA), support vector regression model (SVR), backpropagation neural network (BPNN), and long short-term memory networks (LSTM) are used to forecast the interval trend and residuals. Third, through interval-valued reconstruction, the results of each single forecasting model for three different decomposition methods are obtained respectively. Finally, the combination forecasting results are obtained by the LSTM, which is employed as an ensemble tool. The empirical analysis results show that our proposed model is significantly superior to some benchmark models in terms of accuracy and stability, and is an effective model for forecasting interval-valued carbon prices.