Hybrid ARIMAX–LSTM Modeling with Elastic Net for Time Series Forecasting the Education Index of Jambi Province - Mhd. Teguh Arrozik; Tri Candra Nur Muhaimin; Melkisedek Sampari Koibur (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2026)
Abstract This study proposes a Hybrid ARIMAX–LSTM framework integrated with Elastic Net regularization to improve the forecasting accuracy of the Education Index of Jambi Province. Annual data from 2010 to 2024 are utilized, with Elastic Net applied to select relevant exogenous variables and mitigate multicollinearity. The modelling strategy combines an ARIMAX (1,0,0) model to capture linear dynamics and the influence of selected explanatory variables, with a Long Short-Term Memory (LSTM) network to learn nonlinear patterns from ARIMAX residuals. The dataset is divided into training and testing subsets, where the model is trained using historical data and subsequently validated on unseen observations to assess its generalization capability. Forecasting performance is evaluated using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) on out-of-sample data for 2023 2024. Empirical results show that the proposed hybrid model with Elastic Net significantly outperforms the hybrid model without regularization, achieving an RMSE of 0.3677, an MAE of 0.2647, and a MAPE of 0.40%. In contrast, the ARIMAX–LSTM model with Elastic Net demonstrates substantially better predictive performance, with an RMSE of 0.0720, an MAE of 0.0714, and a MAPE of 0.11%. These findings demonstrate that Elastic Net enhances model generalization and improves residual learning in the LSTM component. After model evaluation, the hybrid models are further employed to generate forecasts of the Education Index for the period 2025–2027 to support medium-term educational planning. Overall, the proposed framework provides a robust and interpretable approach for forecasting regional educational indicators.