Enhanced forecasting method for realized volatility of energy futures prices: A secondary decomposition-based deep learning model

To accurately measure and predict the volatility of energy futures prices, this study employs 5-min high-frequency price data to construct the realized volatility (RV) of crude oil futures and natural gas futures. On this basis, a deep learning model based on secondary decomposition with multi-feature input and single-target output is proposed for multi-step ahead forecasting of RV of energy futures prices. First, the original RV sequence of energy futures is initially decomposed using successive variational mode decomposition (SVMD) to obtain several subsequences. Then, a secondary decomposition of the residual series that cannot be handled by SVMD is performed using improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) to further extract finer features and modes. Afterward, by using multi-feature input and single-feature output, all the subsequences obtained from the two decompositions are input into the deep learning model consisting of spatial transformer network (STN) and convolutional long short-term memory (convLSTM) to obtain the prediction results of each subsequence individually. Finally, the prediction results of all subsequences are ensembled to obtain the final multi-step ahead prediction results of energy futures RV. By introducing the multi-horizon model confidence set (multi-horizon MCS) test, it is statistically confirmed that the proposed multi-feature input and single-target output SVMD-ICEEMDAN-STN-convLSTM model possesses the most superior joint prediction performance in multi-step ahead forecasting of the RV of energy futures prices. Overall, the application of this model holds substantial value and significance, promising to significantly contribute to the sound operation and development of the energy futures market.