Abstract
Abstract
Accurate crude oil price forecasting remains a challenging task due to the nonlinear, non-stationary, and highly volatile nature of financial time series. To address these challenges, this study proposes a hybrid PSO-VMD-LSTM framework that integrates Particle Swarm Optimization (PSO), Variational Mode Decomposition (VMD), and Long Short-Term Memory (LSTM) networks. In the proposed framework, PSO is employed to optimize the key VMD parameters, namely the number of decomposition modes ($K$) and the penalty factor ($\alpha$), while four alternative fitness functions—Envelope Entropy, Sample Entropy, Permutation Entropy, and Reconstruction Error—are systematically evaluated. The decomposed intrinsic mode functions are then used as inputs to the LSTM model for crude oil price forecasting. Experimental results demonstrate that the choice of the fitness function has a significant impact on forecasting performance. Among all evaluated criteria, Reconstruction Error achieved the best results with an RMSE of 1.5444, an MAE of 1.1020, a MAPE of 1.37\%, and an $R^2$ of 0.9859, substantially outperforming the entropy-based alternatives. The findings indicate that preserving the information contained in the original signal is more effective than entropy-based optimization for VMD parameter selection in crude oil price forecasting. Overall, the proposed PSO-VMD-LSTM framework provides an accurate and robust solution for nonlinear financial time series forecasting and offers a promising optimization strategy for decomposition-based predictive models.
JEL Classification: C22 , C45 , C61 , Q41