Carbon Price Forecasting Based on Multi-Resolution Singular Value Decomposition and Extreme Learning Machine Optimized by the Moth–Flame Optimization Algorithm Considering Energy and Economic Factors

Abstract

Carbon price forecasting is significant to both policy makers and market participants. However, since the complex characteristics of carbon prices are affected by many factors, it may be hard for a single prediction model to obtain high-precision results. As a consequence, a new hybrid model based on multi-resolution singular value decomposition (MRSVD) and the extreme learning machine (ELM) optimized by moth–flame optimization (MFO) is proposed for carbon price prediction. First, through the augmented Dickey–Fuller test (ADF), cointegration test and Granger causality test, the external factors of the carbon price, which includes energy and economic factors, are selected in turn. To select the internal factors of the carbon price, the carbon price series are decomposed by MRSVD, and the lags are determined by partial autocorrelation function (PACF). MFO is then used for the optimization of ELM parameters, and external and internal factors are input to the MFO-ELM. Finally, to test the capability and effectiveness of the proposed model, MRSVD-MFO-ELM and its comparison models are used for carbon price forecast in the European Union (EU) and China, respectively. The results show that the performance of the model is significantly better than other models.