A Stacked ARIMA-GRU meta-model for mortality modelling: An Ensemble Learning Approach

Accurate mortality forecasting is essential for effective public health planning and demographic analysis, yet it is challenged by nonlinear and age-dependent patterns in mortality data. This study proposes a stacked ARIMA-GRU ensemble model for age-specific mortality forecasting in Nigeria. The model combines the linear modelling strength of the Autoregressive Integrated Moving Average (ARIMA) model and the nonlinear learning capability of the Gated Recurrent Unit (GRU) network, with Extreme Gradient Boosting (XGBoost) used as a meta-learner. Annual age-specific mortality data for Nigeria covering the period 1950-2023 were obtained from the United Nations World Population Prospects database. Model performance was evaluated using out-of-sample forecasts across all age groups based on Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). The proposed stacked ensemble model achieved the lowest average errors (MAE =0.000929, RMSE =0.001344, MAPE = 2.42%) outperforming ARIMA (MAE =0.002096, RMSE =0.003426, MAPE = 4.95%) and GRU (MAE =0.006837, RMSE =0.008005, MAPE = 10.76%). The results demonstrate the effectiveness of the proposed stacked ensemble learning method for improving mortality forecasting accuracy in Nigeria.