A Hybrid LSTM Neural Network Approach for Modeling Periodical Long-Memory Characteristics in Financial Energy Index Time Series

Forecasting financial market volatility has always been a major challenge in economics and financial engineering. In this study, a hybrid approach based on FIGARCH and PLM-GARCH models combined with Long Short-Term Memory (LSTM) neural networks is proposed for modeling financial time series. The analyzed dataset of the Iran energy index covers October 30, 2016, to January 25, 2023 with 1396 observations. The PLM-GARCH model is capable of identifying long-term dependencies and periodic structures in the conditional variance of time series, while the LSTM network improves prediction accuracy by learning complex and nonlinear patterns. In this approach, the PLM-GARCH model is first used to estimate volatility, and then the residuals from the model are fed as inputs into the LSTM network to extract nonlinear behaviors. Experimental results showed that the combined PLM- GARCH-LSTM model (RMSE = 0.00209, MAPE ≈ 5.1%) outperforms the FIGARCH-LSTM model (RMSE = 0.00224, MAPE ≈ 5.8%) and significantly improves prediction accuracy. These find- ings suggest that combining econometric periodic methods with deep learning can be a powerful tool for forecasting financial volatility.