Abstract

This study presents a predictive modeling framework for forecasting the E-Government Development Index (EGDI) using two advanced time series approaches. Firstly, the Seasonal Auto Regressive Integrated Moving Average with Exogenous Variables (SARIMAX). Secondly, hybrid ARIMA-LSTM model. We focus on two case studies, Iraq and Tunisia, based on monthly EGDI data from the United Nations Survey Reports, spanning the years 2003 to 2024. Using several preprocessing steps such as handling missing data, testing for stationarity using the combined ADF and KPSS tests, and determining the optimal ARIMA parameters through ACF and PACF analysis and implementing autoarima. The model was built and trained using 80% of the data, while 20% was retained for testing. The independence of the residuals verified using the Ljung-Box test. Four types of visualization and error analysis were applied using ACF/PACF for residuals, error plots as prediction error plot, error distribution plot (histogram + KDE) and decomposition analysis to visually assess model fit. Evaluation was conducts using multiple error metrics, including RMSE, MAE, MAPE, MHE, AIC, BIC and MAPA. After building the four models, we ensured that the results and reconstructions were evaluated using the 12 tests we mentioned, and that they were based on the best results and were consensus acceptable. ARIMAX model demonstrated superior performance, achieving an average absolute percentage Accuracy (MAPA) of 98.35% for Iraq and 97.93% for Tunisia. In comparison, the hybrid ARIMA-LSTM model, which combines linear ARIMA outputs with nonlinear corrections from an LSTM neural network, demonstrated competitive predictive ability with a MAPA of 95.68% for Iraq and 96.14% for Tunisia.  SARIMAX showed slightly outperformed the hybrid model in overall accuracy. On other hand, ARIMA-LSTM model demonstrated robustness in capturing complex nonlinear dynamics particularly in the more structurally diverse Tunisian dataset. These results confirm the potential of both models as effective tools for predicting EGDIs and support their application in digital governance planning and policymaking. We designed and we recommend adopting our "12 -Test Approach" for evaluation framework as a standard methodology in future studies addressing analysis and forecasting, and its suitability for different types of time series models. This approach provides comprehensiveness, accuracy, and flexibility in evaluation, regardless of model type or application area.