A hybrid model for carbon price forecasting using GARCH and long short-term memory network

The reform of the EU ETS markets in 2017 has induced new carbon price forecasting challenges. This study proposes a novel decomposition-ensemble paradigm VMD-GARCH/LSTM-LSTM model to better adapt to the current fast-rising and volatile carbon price. Three significant steps are involved: (1) the Variational Mode Decomposition (VMD) algorithm decomposes the carbon price series into sub-modes; (2) The Long Short-Term Memory (LSTM) network predicts low-frequency sub-modes, with the GARCH model predicting high-frequency sub-modes; (3) the forecasts from sub-modes are ensembled through the LSTM non-linear ensemble method. Combining econometric and artificial intelligence methods, our proposed model has an excellent performance on the current carbon price, with smaller errors than single econometrics or AI models or decomposition-ensemble models with linear simple superposition approaches. VMD have significant advantages over their alternative algorithms. Moreover, the LSTM involved in our model is well suited to forecast the rising carbon price in late EU ETS Phase III, providing good insight into risk aversion for participants.