Indonesia’s total fertility rate (TFR) using the brown and holt double exponential smoothing with grid search

Abstract

The Brown and Holt DES method effectively captures trends in time-series data. Its forecasting accuracy heavily depends on the selection of optimal smoothing parameters. Often, the smoothing parameters are selected manually using trial and error methods. This method is time-consuming, unsystematic, prone to bias, not scalable, less reproducible, and increases the risk of overfitting or underfitting. To overcome these problems, in this study, we propose optimization of smoothing parameters using Grid Search. This new approach will be applied to predict Indonesia’s TFR. Grid Search optimization is employed to systematically explore the parameter space and identify the best combination that minimizes forecasting errors. To ensure model robustness, cross-validation is implemented, allowing the evaluation of model performance across multiple training and validation splits. The results show that the Holt DES method with Grid Search is more accurate than the Brown DES with Grid Search, with the smallest Mean Absolute Percentage Error (MSE) value of 0.00972 at  and . Predictions with Holt DES with Grid Search show a downward trend in the national TFR until 2027, potentially falling below the ideal level of 2.1. TFR predictions at the provincial level show pattern variations, with several regions experiencing significant declines. The difference in results between the Brown and Holt methods emphasizes the importance of optimizing smoothing parameters and selecting an appropriate population-analysis prediction model to support demographic policy.