Optimizing Time Series Models for Forecasting Environmental Variables: A Rainfall Case Study

Abstract

The application of time series models for forecasting environmental variables such as precipitation is essential for understanding climatic patterns and supporting sustainable urban planning in environments characterized by high or moderate levels of risk. This study aims to evaluate and optimize time series forecasting models for rainfall prediction in Barranquilla, Colombia. To this end, five models were applied, namely, Simple Moving Average (SMA), Weighted Moving Average (WMA), Exponential Smoothing (ES), and multiplicative and additive Holt–Winters models, using 139 monthly precipitation records from the IDEAM database covering the period 2013–2025. Model accuracy was evaluated using Mean Absolute Error (MAE) and Mean Squared Error (MSE), and nonlinear optimization techniques were applied to estimate smoothing and weighting parameters for improved accuracy. The results showed that optimization significantly enhances model performance, particularly in the multiplicative Holt–Winters model, which achieved the lowest errors, with a minimum MAE of 75.33 mm and an MSE of 9647.07. The comparative analysis with previous studies demonstrated that even simple models can yield substantial improvements when properly optimized. Furthermore, forecasts optimized using MAE were more stable and consistent, whereas those optimized with MSE were more sensitive to extreme variations. Overall, the findings confirm that seasonal models with optimized parameters offer superior predictive capacity, making them valuable tools for hydrological risk management.